Abstract

The prevalent fashion of executing Rydberg-mediated two- and multi-qubit quantum gates in neutral atomic systems is to pump Rydberg excitations using multistep piecewise pulses in the Rydberg blockade regime. Here, we propose to synthesize a Λ-type Rydberg antiblockade (RAB) of two neutral atoms using periodic fields, which facilitates one-step implementations of SWAP and controlled-SWAP (CSWAP) gates with the same gate time. Besides, the RAB condition is modified so as to circumvent the sensitivity of RAB-based gates to infidelity factors, including atomic decay, motional dephasing, and interatomic distance deviation. Our work makes up the absence of one-step schemes of Rydberg-mediated SWAP and CSWAP gates and may pave a way to enhance the robustness of RAB-based gates.

© 2021 Chinese Laser Press

1. INTRODUCTION

The interaction between neutral atoms excited to Rydberg states is strong and long-range, making Rydberg atoms attractive in the context of quantum technologies [14]. Rydberg atoms have been considered as an attractive candidate platform for quantum computing [57] and quantum simulating [810] because of remarkable and continuous advances in cooling, trapping, and manipulating neutral atoms. Entangled states with scale up to 20 qubits have been generated in arrays of Rydberg atoms [11]. Furthermore, atomic species in experiments have been generalized from alkali metal atoms to alkaline earth atoms [12]. Although various schemes have been put forward to implement Rydberg-mediated quantum gates since the pioneering protocol was reported [13], enormous challenges remain in achieving experimentally high-fidelity Rydberg gates as well as in highly efficient Rydberg-atom-based quantum computing [14]. On the one hand, the gate fidelity is always limited due to intrinsic and technical errors. Intrinsic errors involve atomic decay and imperfect approximate conditions, including blockade errors in the Rydberg blockade [1,1416] gate schemes [13,1720], nonadiabatic errors [21,22] in adiabatic gate schemes [13,2327], and higher-order perturbation errors in Rydberg antiblockade (RAB) [2833] gate schemes [3440]. Technical errors are caused by imperfections of techniques in, e.g., cooling, trapping, and manipulating atoms [1,2,41,42]. On the other hand, existing schemes are not sufficient for one-step implementing certain two-qubit gates and many multi-qubit gates, especially for some frequently used gates, such as the SWAP gate, and the controlled-SWAP (CSWAP), that is, the Fredkin gate [43].

Despite a controlled-not (CNOT) gate combined with a small number of single-qubit gates constructing arbitrary gate operations (e.g., a SWAP gate formed with three CNOT gates [44]), direct executions of quantum gates can significantly improve the processing efficiency of lengthy quantum algorithms rather than decomposing them into a series of elementary gates [25,4548]. The SWAP gate is an important, nontrivial two-qubit gate with extensive applications in quantum computation [49], entanglement swapping [50], and quantum repeaters [51]. The CSWAP gate is one of the most representative multi-qubit gates, swapping the quantum states of two target qubits depending on the state of a control qubit, which holds important functions in quantum error correction [52], quantum fingerprinting [53], and quantum routers [54]. Among existing Rydberg-mediated gate schemes, SWAP gates are achieved in three or more steps, using multiple piecewise pulses and involving two or more Rydberg states in single atoms [5557]. The scheme of implementing a CSWAP gate requires five-step operations with five piecewise pulses [58]. The multistep operations of implementing quantum gates not only make quantum algorithms rigmarole and unproductive but also accumulate more decoherence.

In the present work, we propose schemes to implement one-step SWAP and CSWAP gates of Rydberg atoms that are driven by periodic amplitude-modulated (AM) fields. The synthetic interplay between AM fields and interatomic Rydberg–Rydberg interaction (RRI) induces a Λ-type RAB structure of two atoms, based on which a SWAP gate on two atoms and a CSWAP gate on three atoms can be formed. However, similar to existing RAB-based gate schemes [3437,59,60], the attendance of a doubly excited Rydberg state |rr during the evolution will induce common issues in RAB-based gates, i.e., the sensitivity to atomic decay, motional dephasing, and interatomic distance deviation. Aiming at these common issues, we modify the RAB condition to constrain the participation of |rr in the gate procedure, which can not only reduce the effect of atomic decay from Rydberg states and of motional dephasing during Rydberg excitation but also loosen the stringent restrictions on the parameter condition of RAB to a certain degree. The present work fills the gap of directly constructing Rydberg-atom SWAP and CSWAP gates in one step. In addition, the work may also pave the way to circumvent the common issues in RAB-based gates.

This paper is organized as follows. In Section 2, we illustrate the construction of a Λ-type RAB structure, based on which one-step SWAP gates are implemented with resonant and modified RAB, respectively. In Section 3, the robustness of two kinds of SWAP gates is studied and compared. In Section 4, we propose to implement a CSWAP gate in one step. A conclusion is given in Section 5.

2. SWAP GATES BASED ON RYDBERG ANTIBLOCKADE

A. Resonant Λ-Type Rydberg Antiblockade

As shown in Fig. 1(a), the interaction of the laser-driven two atoms is described by the Hamiltonian (=1)

H^12=H^1I^2+I^1H^2+V|rrrr|,
where V|rrrr| with |rr|r1|r2 denotes the two-atom RRI, and I^j (j=1,2) is the identity operator of the jth atom. H^j, the individual Hamiltonian of the jth laser-driven atom, reads
H^j=k=01Ωk(t)2|kjr|+H.c.
We impose resonant AM laser fields on the two atoms to induce AM Rabi frequencies Ωk(t)=Ωkmcos(ωkt) (k=0,1), where Ωkm is the maximum and ωk the modulation frequency. We separate V into V=δ+δ0, where we define δω1ω0 whose function is to compensate for the detuning of the transition |01(|10)|rr so as to induce the RAB, while δ0 is a small quantity with δδ0 whose function is to neutralize the Stark shift of |rr cased by the AM fields. When considering the parameter condition |ω0|,|ω1|,|ω0δ|,|ω1+δ||Ω0m|/4,|Ω1m|/4, with the second-order perturbation theory [61,62] the two-atom Hamiltonian can be reduced toward an effective form (see Appendix A):
H^e=[Ωe2(|01rr|+|10rr|)+H.c.]+δ|rrrr|,
in which Ωe=Ω0mΩ1m/8ω1Ω0mΩ1m/8ω0 is the effective Rabi frequency of the second-order double Rydberg pumping, and δ=Δrr+δ0 with Δrr=Ω0m2/8ω1Ω1m2/8ω0+Ω1m2/8(ω1+δ)Ω0m2/8(ω0δ) being the Stark shift of the Rydberg pair state |rr.
 figure: Fig. 1.

Fig. 1. (a) Schematic for implementing a SWAP gate. Two identical atoms are driven resonantly by two AM laser fields, excited from two ground (computational) states |0 and |1 to a Rydberg (mediated) state |r, respectively, with modulated Rabi frequencies Ω0(t) and Ω1(t). Two atoms are coupled to each other by RRI with strength V=C6/d6, C6 being the van der Waals coefficient and d the interatomic distance. The effective Λ-type RAB dynamics is shown in the shadow of (b). (b) Schematic for implementing a CSWAP gate. Inset circle: the control atom c is coupled to target atoms 1 and 2 described in (a), with RRI strengths V1c and V2c corresponding to interatomic distances d1c and d2c, respectively. The effective Λ-type system of the target atoms is coupled to the control atom with RRI strength (V1c+V2c). In addition, the control atom is excited resonantly by another AM field from |0c to |rc with Rabi frequency Ωc(t).

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The effective quantum system described by Eq. (3) indicates a Λ-type RAB structure where the doubly excited Rydberg pair state |rr mediates the transition between two odd-parity computational states |01 and |10, while even-parity states |00 and |11 remain unaffected. A SWAP gate can be implemented through a resonant Raman-like process |01|rr|10 with the resonance condition δ=0 and gate time T=2π/|Ωe|; further, the SWAP gate is of the form USWAP=|0000||0110||1001|+|1111|, which is equivalent to the standard form up to local phase operations.

For identifying the gate validity, we simulate numerically the gate performance by solving the master equation

ρ˙=i[ρ,H^Full]12j=1Nk=02(L^kjL^kjρ2L^kjρL^kj+ρL^kjL^kj),
in which ρ is the density operator and ρ˙ the time derivative of the density operator. H^Full denotes the full Hamiltonian of the atomic system [for the SWAP gate H^Full is Eq. (1)]. N=2 (N=3) is the number of atoms for the SWAP (CSWAP) gate. The atomic decay operator is defined by L^kjγk|kjr|, for which an additional ground state |2j is introduced to denote those Zeeman magnetic sublevels out of the computational states |0j and |1j. In this work, we assume that Rb87 atoms are adopted, and decay rates from a Rydberg state into eight Zeeman ground states are identical for convenience, so γ0=γ1=1/8τ and γ2=3/4τ with τ being the lifetime of the Rydberg state.

The computational states can be encoded on the hyperfine ground states |0=|5S1/2,F=1,mF=0 and |1=|5S1/2,F=2,mF=0. We choose a suitable set of parameters Ω0m/2π=5.6MHz, Ω1m/2π=16.4MHz, ω0m/2π=40MHz, and ω1m/2π=110MHz, which gives |Ωe|/2π=183.6kHz, T=3.872μs, and Δrr/2π=487.4kHz. For δ=0, V/2π=70.49MHz can be attained, which is experimentally feasible, for example, with {|r=|70S1/2 (C6/2π=858.4GHz·μm6), d4.8μm} or {|r=|100S1/2 (C6/2π=56.2THz·μm6), d9.6μm}. To illustrate performance of the SWAP gate, in Fig. 2 we numerically calculate the trace-preserving-quantum-operator-based average fidelity [34,38,63] (see Appendix B for definition). The average fidelity of the SWAP gate with δ=0 reaches >0.995.

 figure: Fig. 2.

Fig. 2. Time-dependent average fidelities of the SWAP gate with {δ=0, T=3.87μs} and {δ/2π=1.11MHz, T=33.28μs}, respectively. Atomic decay is not considered.

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B. Modified Condition of Rydberg Antiblockade

The SWAP gate noted above is not robust. The Rydberg pair state |rr attends significantly the gate procedure, which will cause nonignorable decay errors. More notably, the gate is sensitive to fluctuations in RRI strength (interatomic distance) and is susceptible to motion-induced dephasing due to finite atomic temperature, which are common and intractable issues in RAB-based gates [3437,40,59,60,64,65] such that to experimentally implement them with a high-fidelity suffers from great difficulties. In order to circumvent these issues, reducing participation of |rr in the gate procedure can be an effective approach [38,66,67], which not only reduces atomic decay errors but also relaxes the demanding RAB condition and weakens effect of motional dephasing. To this end, we consider the large-detuning condition |δ||Ωe|/2 for the Λ-type RAB structure described by Eq. (3). Then, a modified format of RAB can be obtained, holding an effective ground-state exchange interaction between two atoms, described by

H^dd=Ωdd2(|01+|10)(01|+10|),
with Ωdd=Ωe2/2δ. Thus, a SWAP gate USWAP can be achieved with gate time T=π/|Ωdd|. With δ/2π=1.11MHz corresponding to T=33.28μs, the average gate fidelity can also reach >0.995 [see Fig. 2]. The modified condition |δ||Ωe|/2 of RAB suppresses the excitation of the doubly excited Rydberg state |rr, which can be found in Fig. 3, where we compare the situations of the resonant RAB [Fig. 3(a)] and the modified RAB [Fig. 3(b)] by plotting Rydberg excitation probabilities with different excitation numbers. From Fig. 3, we learn that the single-excitation states are hardly populated for both cases. More importantly, the double-excitation Rydberg pair state |rr is significantly constrained for the modified RAB, and its excitation probability is less than 0.015 throughout the gate procedure.
 figure: Fig. 3.

Fig. 3. Rydberg excitation probabilities during the SWAP gate procedure with different excitation numbers for (a) the resonant RAB with δ=0 and (b) the modified RAB with δ/2π=1.11MHz, respectively. Two-atom initial product state |Ψ0=(|01+|11)/2|12 is specified.

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3. SWAP GATE WITH MODIFIED ROBUSTNESS

For the conventional Rydberg-antiblockade quantum gates, a key property is the participation of the Rydberg pair state |rr in the gate procedure mediating the state shifts of ground states, so the gate operations on atomic ground states suffer from decay from Rydberg states, laser dephasing caused by atomic motions due to the Doppler effect. Besides, to guarantee the attendance of |rr, the RAB condition with a strict relation among ω0, ω1, and V must be precisely controlled, which makes the gate operations sensitive to errors in V. However, for the modified RAB described by the effective Hamiltonian in Eq. (5), |rr is not needed in the gate procedure, so the issues above will be efficiently evaded.

In the following, we investigate and compare infidelities of the SWAP gates obtained by the resonant RAB and the modified RAB, taking into account atomic decay originated from a finite lifetime of the Rydberg state, motional dephasing due to finite atomic temperature, and fluctuations in RRI strength caused by interatomic distance deviation. For simplicity, a two-atom initial product state |Ψ0=(|01+|11)/2|12 is specified, and the gate fidelity is defined by Ftr(ρ|ΨΨ|) with |Ψ=USWAP|Ψ0. From Fig. 4(a), we learn that the infidelity of the SWAP gate obtained by the modified RAB is reduced compared with that obtained by the resonant RAB, even though the gate time is prolonged by near 10 multiples. The gate infidelity for the modified RAB can decrease to below 103 with τ>500μs.

 figure: Fig. 4.

Fig. 4. Infidelities of the SWAP gates caused by (a) atomic decay with different lifetimes of the Rydberg state, (b) motional dephasing with different atomic temperatures, (c) standard deviations of the interatomic distance, and (d) deviations in the RRI strength. Each point in (b), (c), and (d) denotes the average of 201 results.

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Due to the atomic thermal motion, processes of Rydberg excitations suffer from motional dephasing inevitably because of presence of the Doppler effect [2,68,69], which is an important resource of technical errors. When considering motional dephasing, the Rabi frequencies of the Rydberg excitation in Eq. (2) are changed, as Ωk(t)Ωk(t)eiΔkt (k=0,1) [42,68,69]. The detunings Δ0,1 of the Rydberg pumping lasers seen by the atoms are two random variables yielded with a Gaussian probability distribution of the mean Δ¯=0 and the standard deviation σΔ=keffvrms, where keff is the effective wave vector magnitude of lasers that atoms undergo, and vrms=kBTa/M is the atomic root-mean-square velocity with kB, Ta, and M being the Boltzmann constant, atomic temperature, and atomic mass, respectively. Here, we suppose for simplicity that there are two counterpropagating laser fields with wavelengths λ1480nm and λ2780nm used for excitation of the Rydberg state |r=|100S1/2 through a two-photon process with the intermediate state |p=|5P3/2 [68], which gives an effective wave vector magnitude keff5×106m1 [42]. Then, with these settings, we numerically work out in Fig. 4(b) the infidelities of the SWAP gates obtained by the resonant RAB and the modified RAB, respectively. The gate infidelity for the modified RAB is dramatically reduced by even an order of magnitude when Ta>30μK, compared with that for the resonant RAB. With an experimentally accessible atomic temperature Ta10μK [5,7], the infidelity caused by motional dephasing can be below 102.

For controlling the RRI strength between the atoms, interatomic distance cannot be strictly fixed owing to imperfections of cooling and trapping atoms, and it can be characterized with a quasi-1D Gaussian probability distribution of the mean (ideal) d=C6/V6 and the standard deviation σd [6]. From Fig. 4(c), we know that, while the gate performance is still sensitive to the interatomic distance deviation, the modified RAB can loosen this sensitivity to a certain degree. More intuitively, we consider a relative deviation δV to change the RRI strength into V[1+rand(δV)], where rand(δV) is a function creating random numbers within [δV,δV]. Figure 4(d) shows the effect of different δV on the fidelities of implementing the SWAP gates. It is apparent that increasing the relative deviation in V reduces the fidelity of the SWAP gates significantly for the case of the resonant RAB, while the effect of δV on the SWAP gate of the modified RAB is much slighter, which indicates that the gate performance against the deviations in V is largely improved by the modified RAB.

4. ONE-STEP IMPLEMENTATION OF CSWAP GATES

Finally, we illustrate one-step implementation of a CSWAP gate, for which a control atom (termed c) is introduced, whose state determines whether or not the SWAP gate on atoms 1 and 2 can be executed. The schematic concerning Rydberg pumping and interatomic RRI is detailed in Fig. 1(b). The interaction of the laser-driven three atoms is described by a full Hamiltonian

H^12c=H^12I^c+I^1I^2H^c+I^1V2c|rr2crr|+V1c|r1r|I^2|rcr|,
where H^12 is given in Eq. (1), and H^c=Ωc(t)|0cr|/2+H.c. with Ωc(t)=Ωcmcos(ωct) modulated in amplitude. On the basis of the SWAP gate, the Hamiltonian Eq. (6) is reduced to
H^12c=H^eI^c+I^1I^2H^c+(V1c+V2c)|rrrrrr|,
where H^e is given in Eq. (3). The diagram of this Hamiltonian is visualized in Fig. 1(b). Furthermore, this three-atom dynamics can be simplified toward the form (see Appendix C)
H^eff=H^e|1c1|,
when considering the condition |ωc||Ωcm|/4 and |Ωcm/4±δ||Ωe|/2 as well as the relation V1c+V2c=ωcΔrrr with Δrrr=Ωe2/2ωc+Ωcm2/32ωc being a small Stark shift of the triply excited Rydberg state |rrr. Equation (8) indicates that when and only when the state of the control atom is |1, the SWAP gate on atoms 1 and 2 works, which is exactly a CSWAP gate UCSWAP=I^1I^2|0c0|+USWAP|1c1|. Besides, according to different assignments of δ in H^e, the CSWAP gate can be implemented based on not only the resonant RAB but also on the modified RAB with enhanced robustness, similar to the implementation of the SWAP gate. In Fig. 5, we numerically calculate the average fidelity of the CSWAP gate achieved by the resonant RAB (δ=0) and the modified RAB (δ/2π=1.11MHz), and two lines both reach high average fidelities >0.991, which is over the error-correction threshold in a surface code scheme [70].
 figure: Fig. 5.

Fig. 5. Time-dependent average fidelities of the CSWAP gate with {δ=0, T=3.87μs} and {δ/2π=1.11MHz, T=33.28μs}, respectively. Atomic decay is not considered. Ωcm/2π=12MHz and ωc/2π=142MHz, and V1c/2π=V2c/2π=70.98MHz.

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From Eq. (8), we know that the triply excited Rydberg state |rrr12c is not involved in the CSWAP gate procedure. Besides, the modified condition |δ||Ωe|/2 of RAB suppresses the excitation of the doubly excited Rydberg state |rr12. For more detailed illustration, in Fig. 6 we calculate numerical Rydberg excitation probabilities with different excitation numbers for cases of the resonant RAB and the modified RAB. From Fig. 6, we learn that the triply excited state |rrr12c is suppressed for both cases. Besides, similar to the SWAP gates, the single-excitation states are also hardly populated for both cases, and the double-excitation state |rr12 is also constrained for the modified RAB, whose excitation probability is always below 0.015.

 figure: Fig. 6.

Fig. 6. Rydberg excitation probabilities during the CSWAP gate procedure with different excitation numbers for (a) the resonant RAB with δ=0 and (b) the modified RAB with δ/2π=1.11MHz, respectively. Three-atom initial product state |Ψ0=(01|11)/2(|02|12)/2(|0c|1c)/2 is specified.

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The CSWAP gate is on the basis of the SWAP gate, so the gate performance is similar to the SWAP gate, including gate time and robustness. Because Rydberg excitation of any one of the three atoms can be avoided for the modified RAB [see Fig. 6(b)], the infidelity caused by atomic decay from Rydberg states into ground states will be negligible. The effect on the CSWAP gate fidelity of motional dephasing that occurs during Rydberg excitation is also slight because only virtual excitation for the three atoms attends throughout the gate procedure. In addition, the infidelity in the case of the modified RAB, caused by moderate fluctuations of distances among the three atoms, will be much less than that in the conventional RAB-based quantum gates. These properties are identified in Fig. 7.

 figure: Fig. 7.

Fig. 7. Infidelities of the CSWAP gates caused by (a) atomic decay with different lifetimes of the Rydberg state, (b) motional dephasing with different atomic temperatures, (c) standard deviations of the distance between the two target atoms, and (d) deviations in the RRI strength between the two target atoms. Each point in (b), (c), and (d) denotes the average of 201 results.

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5. CONCLUSION

To conclude, we have proposed effective schemes to implement one-step Rydberg-mediated SWAP and CSWAP gates on neutral atomic systems under a Rydberg antiblockade regime. The use of resonant amplitude-modulated fields enables a Λ-type Rydberg antiblockade structure, which facilitates a Raman-like process connecting two odd-parity computational states of two atoms and thus the implementation of the SWAP gate. Besides, the robustness of gates is enhanced through modifying the condition of the Rydberg antiblockade. The introduction of a periodically driven control atom makes the execution of the SWAP gate depend on the state of the control atom, so a CSWAP gate is achieved with the same gate time and similar gate performance to the SWAP gate. Our work fills the gap of directly implementing one-step Rydberg-mediated SWAP and CSWAP gates and circumvents common issues in Rydberg antiblockade based gates.

APPENDIX A: DERIVATION OF EQ. (3)

With the two-atom basis {|jk} (j,k=0,1,r), the full Hamiltonian of two atoms is

H^0=12[Ω0mcos(ω0t)(|00r0|+|01r1|+|0rrr|+|000r|+|101r|+|r0rr|)+Ω1mcos(ω1t)(|10r0|+|11r1|+|1rrr|+|010r|+|111r|+|r1rr|)+H.c.]+V|rrrr|.
We transform Eq. (A1) into the frame defined by U^0=exp(itδ|rrrr|) with δ=Vδ0=ω1ω0δ0 and obtain H^1=U^0(H^0it)U^0=H^1+δ0|rrrr| with
H^1=Ω0m4{(eiω0t+eiω0t)(|00r0|+|01r1|+|000r|+|101r|)+[ei(ω0δ)t+eiω1t](|0rrr|+|r0rr|)}+Ω1m4{(eiω1t+eiω1t)(|10r0|+|11r1|+|010r|+|111r|)+[eiω0t+ei(ω1+δ)t](|1rrr|+|r1rr|)}+H.c.
When considering |ω0|,|ω1|,|ω0δ|,|ω1+δ||Ω0m|/4, |Ω1m|/4, the terms
Ω0m4(eiω0t+eiω0t)(|00r0|+|000r|)+Ω1m4(eiω1t+eiω1t)(|11r1|+|111r|)+H.c.
can be neglected under the rotating-wave approximation because the transitions are of large detunings; besides, the involved even-parity states, |00 and |11, cannot be effectively coupled resonantly to other states yet through two-photon processes. In addition, under the second-order perturbation theory, the even-parity computational states |00 and |11 have a zero-value sum of Stark shifts, and all single-excitation states are uncoupled to the four computational states. Then, the remaining part of Eq. (A2) can be sorted as
H^1[Ω0m4(eiω0t+eiω0t)|01r1|+Ω1m4eiω0t|r1rr|]+[Ω1m4(eiω1t+eiω1t)|010r|+Ω0m4eiω1t|0rrr|]+[Ω0m4(eiω0t+eiω0t)|101r|+Ω1m4eiω0t|1rrr|]+[Ω1m4(eiω1t+eiω1t)|10r0|+Ω0m4eiω0t|r0rr|]+Ω0m4ei(ω0δ)t(|0rrr|+|r0rr|)+Ω1m4ei(ω1+δ)t(|1rrr|+|r1rr|)+H.c.
With the second-order perturbation theory, the first four terms in Eq. (A3) induce the effective coupling of |01|rr|10 and Stark shifts of |rr, while the last two terms induce solely Stark shifts of |rr. Therefore, a final effective Hamiltonian of the two atoms can be obtained as
H^e=[Ωe2(|01rr|+|10rr|)+H.c.]+δ|rrrr|,
in which Ωe=Ω0mΩ1m/8ω1Ω0mΩ1m/8ω0 and δ=Δrr+δ0 with Δrr=Ω0m2/8ω1Ω1m2/8ω0+Ω1m2/8(ω1+δ)Ω0m2/8(ω0δ) being the sum Stark shift of |rr.

APPENDIX B: DEFINITION OF THE TRACE-PRESERVING-QUANTUM-OPERATOR-BASED AVERAGE FIDELITY

According to Nielsen's work [63], the trace-preserving-quantum-operator-based average fidelity of a quantum gate is defined as

F¯(ε,U^)={j=14Ntr[U^u^jU^ε(u^j)]+l2}/l2(l+1),
where U^ is the ideal gate, u^j=kNσ^k is the tensor of Pauli matrices σ^k{I^,σ^x,σ^y,σ^z} on computational states {|0, |1}, and l=2N for an N-qubit gate. ε(u^j) is a trace-preserving quantum operation obtained through our logic gates that can be solved by the master equation.

APPENDIX C: DERIVATION OF EQ. (8)

First, it is clear that the evolution from three-atom computational states |00112c and |11112c is prohibited. For |00012c or |11012c, the governing Hamiltonian is H^β0=Ωcm(eiωct+eiωct)|β012cβr|/4+H.c. (β=00,11). No evolution will occur when |ωc||Ωcm|/4 is considered, because the laser-induced transitions are largely detuned, and the sum Stark shift of |β012c is zero.

When the state of three atoms is |01012c or |10012c, the governing Hamiltonian of the three atoms is H^2=H^2+δ|rr12rr|+(V1c+V2c)|rrr12crrr| with

H^2=Ωcm4(eiωct+eiωct)(|01012c01r|+|10012c10r|+|rr012crrr|)+Ωe2(|01012crr0|+|10012crr0|+|01r12crrr|+|10r12crrr|)+H.c.
Transforming H^2 to the frame defined by U^1=exp(itωc|rrr12crrr|), one can obtain H^3=H^3+δ|rr12rr|+(V1c+V2cωc)|rrr12crrr| with
H^3=Ωcm4[(eiωct+eiωct)(|01012c01r|+|10012c10r|)+(1+e2iωct)|rr012crrr|]+Ωe2(|01012crr0|+|10012crr0|+|01r12crrr|eiωct+|10r12crrr|eiωct)+H.c.
Through neglecting frequent oscillations under rotating-wave approximation with the condition |ωc||Ωcm|/4,|Ωe|/2, H^3 becomes
H^3=[Ωcm4|rr012crrr|+Ωe2(|01012crr0|+|10012crr0|)+H.c.]+Δrrr|rrr12crrr|,
with Δrrr=Ωe2/2ωc+Ωcm2/32ωc being the Stark shift of |rrr12c. In this case, an effective three-atom Hamiltonian of H^3 can be obtained as H^4=H^3+δ|rr12rr| with the condition V1c+V2c=ωcΔrrr. H^4 can be rewritten as
H^4=[Ωe2(|01012c+|10012c)(ϕ0|+ϕ1|)+H.c.]+Ωcm4n=01(1)n|ϕnϕn|+δ|rr12rr|,
in which |ϕn=(|rr012c+(1)n|rrr12c)/2. Transforming H^4 to the frame defined by U^2=exp(itA^) with A^=Ωcmn=01(1)n|ϕnϕn|/4+δ|rr12rr|, one can obtain a Hamiltonian with entirely off-resonant interactions
H^5=Ωe2(|01012c+|10012c)[ϕ0|eit(Ωcm/4+δ)+ϕ1|eit(Ωcm/4δ)]+H.c.
When the condition |Ωcm/4±δ||Ωe|/2 is satisfied, transitions from |01012c or |10012c can be banned.

Now that the evolution from six three-atom computational states, including |00012c, |01012c, |10012c, |11012c, |00112c, and |11112c, is banned, the dynamics of the three atoms can be governed by an effective Hamiltonian

H^eff=[Ωe2(|01112c+|10112c)rr1|+H.c.]+δ|rr112crr1|,
which is exactly Eq. (8) in the main text.

Funding

National Natural Science Foundation of China (NSFC) (11675046, 21973023, 11804308); Program for Innovation Research of Science in Harbin Institute of Technology (A201412); Postdoctoral Scientific Research Developmental Fund of Heilongjiang Province (LBH-Q15060); Natural Science Foundation of Henan Province (202300410481).

Disclosures

The authors declare no conflicts of interest.

REFERENCES

1. M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010). [CrossRef]  

2. M. Saffman, “Quantum computing with atomic qubits and Rydberg interactions: progress and challenges,” J. Phys. B 49, 202001 (2016). [CrossRef]  

3. A. Browaeys and T. Lahaye, “Many-body physics with individually controlled Rydberg atoms,” Nat. Phys. 16, 132–142 (2020). [CrossRef]  

4. Z.-Y. Zhang, T.-Y. Zhang, Z.-K. Liu, D.-S. Ding, and B.-S. Shi, “Research progress of Rydberg many-body interaction,” Acta Phys. Sin. 69, 080301 (2020). [CrossRef]  

5. H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018). [CrossRef]  

6. T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019). [CrossRef]  

7. H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019). [CrossRef]  

8. P. Schau, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015). [CrossRef]  

9. H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016). [CrossRef]  

10. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017). [CrossRef]  

11. A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019). [CrossRef]  

12. I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020). [CrossRef]  

13. D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000). [CrossRef]  

14. M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001). [CrossRef]  

15. E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009). [CrossRef]  

16. A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009). [CrossRef]  

17. X.-F. Shi, “Deutsch, Toffoli, and CNOT gates via Rydberg blockade of neutral atoms,” Phys. Rev. Appl. 9, 051001 (2018). [CrossRef]  

18. C.-P. Shen, J.-L. Wu, S.-L. Su, and E. Liang, “Construction of robust Rydberg controlled-phase gates,” Opt. Lett. 44, 2036–2039 (2019). [CrossRef]  

19. K.-Y. Liao, X.-H. Liu, Z. Li, and Y.-X. Du, “Geometric Rydberg quantum gate with shortcuts to adiabaticity,” Opt. Lett. 44, 4801–4804 (2019). [CrossRef]  

20. B.-J. Liu, S.-L. Su, and M.-H. Yung, “Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms,” Phys. Rev. Res. 2, 043130 (2020). [CrossRef]  

21. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998). [CrossRef]  

22. N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89, 015006 (2017). [CrossRef]  

23. D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, “High-fidelity Rydberg quantum gate via a two-atom dark state,” Phys. Rev. A 96, 042306 (2017). [CrossRef]  

24. I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018). [CrossRef]  

25. M. Khazali and K. Mølmer, “Fast multiqubit gates by adiabatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits,” Phys. Rev. X 10, 021054 (2020). [CrossRef]  

26. M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, “Symmetric Rydberg controlled-Z gates with adiabatic pulses,” Phys. Rev. A 101, 062309 (2020). [CrossRef]  

27. A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020). [CrossRef]  

28. C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98, 023002 (2007). [CrossRef]  

29. T. Pohl and P. R. Berman, “Breaking the dipole blockade: nearly resonant dipole interactions in few-atom systems,” Phys. Rev. Lett. 102, 013004 (2009). [CrossRef]  

30. J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009). [CrossRef]  

31. T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104, 013001 (2010). [CrossRef]  

32. W. Li, C. Ates, and I. Lesanovsky, “Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps,” Phys. Rev. Lett. 110, 213005 (2013). [CrossRef]  

33. S. Basak, Y. Chougale, and R. Nath, “Periodically driven array of single Rydberg atoms,” Phys. Rev. Lett. 120, 123204 (2018). [CrossRef]  

34. S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016). [CrossRef]  

35. S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, “One-step construction of the multiple-qubit Rydberg controlled-phase gate,” Phys. Rev. A 98, 032306 (2018). [CrossRef]  

36. J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, “Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45, 1200–1203 (2020). [CrossRef]  

37. T. H. Xing, X. Wu, and G. F. Xu, “Nonadiabatic holonomic three-qubit controlled gates realized by one-shot implementation,” Phys. Rev. A 101, 012306 (2020). [CrossRef]  

38. H.-D. Yin, X.-X. Li, G.-C. Wang, and X.-Q. Shao, “One-step implementation of Toffoli gate for neutral atoms based on unconventional Rydberg pumping,” Opt. Express 28, 35576–35587 (2020). [CrossRef]  

39. J.-L. Wu, J. Song, and S.-L. Su, “Resonant-interaction-induced Rydberg antiblockade and its applications,” Phys. Lett. A 384, 126039 (2020). [CrossRef]  

40. S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020). [CrossRef]  

41. M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, “Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms,” J. Phys. Conf. Ser. 264, 012023 (2011). [CrossRef]  

42. S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, “Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states,” Phys. Rev. A 97, 053803 (2018). [CrossRef]  

43. E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1983). [CrossRef]  

44. N. Schuch and J. Siewert, “Natural two-qubit gate for quantum computation using the XY interaction,” Phys. Rev. A 67, 032301 (2003). [CrossRef]  

45. L. Isenhower, M. Saffman, and K. Mølmer, “Multibit CkNOT quantum gates via Rydberg blockade,” Quantum Inf. Process. 10, 755 (2011). [CrossRef]  

46. R. J. Spiteri, M. Schmidt, J. Ghosh, E. Zahedinejad, and B. C. Sanders, “Quantum control for high-fidelity multi-qubit gates,” New J. Phys. 20, 113009 (2018). [CrossRef]  

47. W. Feng and D.-W. Wang, “Quantum Fredkin gate based on synthetic three-body interactions in superconducting circuits,” Phys. Rev. A 101, 062312 (2020). [CrossRef]  

48. S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, “Single-step implementation of high-fidelity n-bit Toffoli gates,” Phys. Rev. A 101, 022308 (2020). [CrossRef]  

49. R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019). [CrossRef]  

50. W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019). [CrossRef]  

51. N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011). [CrossRef]  

52. I. L. Chuang and Y. Yamamoto, “Quantum bit regeneration,” Phys. Rev. Lett. 76, 4281–4284 (1996). [CrossRef]  

53. H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87, 167902 (2001). [CrossRef]  

54. B. K. Behera, T. Reza, A. Gupta, and P. K. Panigrahi, “Designing quantum router in IBM quantum computer,” Quantum Inf. Process. 18, 328 (2019). [CrossRef]  

55. H.-Z. Wu, Z.-B. Yang, and S.-B. Zheng, “Quantum state swap for two trapped Rydberg atoms,” Chin. Phys. B 21, 040305 (2012). [CrossRef]  

56. X.-F. Shi, F. Bariani, and T. A. B. Kennedy, “Entanglement of neutral-atom chains by spin-exchange Rydberg interaction,” Phys. Rev. A 90, 062327 (2014). [CrossRef]  

57. A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015). [CrossRef]  

58. M. Gärttner, K. P. Heeg, T. Gasenzer, and J. Evers, “Dynamic formation of Rydberg aggregates at off-resonant excitation,” Phys. Rev. A 88, 043410 (2013). [CrossRef]  

59. S.-L. Su, Y. Gao, E. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95, 022319 (2017). [CrossRef]  

60. X.-Y. Zhu, E. Liang, and S.-L. Su, “Rydberg-atom-based controlled arbitrary-phase gate and its applications,” J. Opt. Soc. Am. B 36, 1937–1944 (2019). [CrossRef]  

61. D. James and J. Jerke, “Effective Hamiltonian theory and its applications in quantum information,” Can. J. Phys. 85, 625–632 (2007). [CrossRef]  

62. W. Shao, C. Wu, and X.-L. Feng, “Generalized James’ effective Hamiltonian method,” Phys. Rev. A 95, 032124 (2017). [CrossRef]  

63. M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303, 249–252 (2002). [CrossRef]  

64. C.-Y. Guo, L.-L. Yan, S. Zhang, S.-L. Su, and W. Li, “Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms,” Phys. Rev. A 102, 042607 (2020). [CrossRef]  

65. F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020). [CrossRef]  

66. E. Brion, L. H. Pedersen, and K. Mølmer, “Implementing a neutral atom Rydberg gate without populating the Rydberg state,” J. Phys. B 40, S159–S166 (2007). [CrossRef]  

67. J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021). [CrossRef]  

68. X.-F. Shi, “Fast, accurate, and realizable two-qubit entangling gates by quantum interference in detuned Rabi cycles of Rydberg atoms,” Phys. Rev. Appl. 11, 044035 (2019). [CrossRef]  

69. X.-F. Shi, “Suppressing motional dephasing of ground-Rydberg transition for high-fidelity quantum control with neutral atoms,” Phys. Rev. Appl. 13, 024008 (2020). [CrossRef]  

70. A. G. Fowler, A. M. Stephens, and P. Groszkowski, “High-threshold universal quantum computation on the surface code,” Phys. Rev. A 80, 052312 (2009). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
    [Crossref]
  2. M. Saffman, “Quantum computing with atomic qubits and Rydberg interactions: progress and challenges,” J. Phys. B 49, 202001 (2016).
    [Crossref]
  3. A. Browaeys and T. Lahaye, “Many-body physics with individually controlled Rydberg atoms,” Nat. Phys. 16, 132–142 (2020).
    [Crossref]
  4. Z.-Y. Zhang, T.-Y. Zhang, Z.-K. Liu, D.-S. Ding, and B.-S. Shi, “Research progress of Rydberg many-body interaction,” Acta Phys. Sin. 69, 080301 (2020).
    [Crossref]
  5. H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
    [Crossref]
  6. T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
    [Crossref]
  7. H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
    [Crossref]
  8. P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
    [Crossref]
  9. H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
    [Crossref]
  10. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
    [Crossref]
  11. A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
    [Crossref]
  12. I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
    [Crossref]
  13. D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000).
    [Crossref]
  14. M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
    [Crossref]
  15. E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
    [Crossref]
  16. A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
    [Crossref]
  17. X.-F. Shi, “Deutsch, Toffoli, and CNOT gates via Rydberg blockade of neutral atoms,” Phys. Rev. Appl. 9, 051001 (2018).
    [Crossref]
  18. C.-P. Shen, J.-L. Wu, S.-L. Su, and E. Liang, “Construction of robust Rydberg controlled-phase gates,” Opt. Lett. 44, 2036–2039 (2019).
    [Crossref]
  19. K.-Y. Liao, X.-H. Liu, Z. Li, and Y.-X. Du, “Geometric Rydberg quantum gate with shortcuts to adiabaticity,” Opt. Lett. 44, 4801–4804 (2019).
    [Crossref]
  20. B.-J. Liu, S.-L. Su, and M.-H. Yung, “Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms,” Phys. Rev. Res. 2, 043130 (2020).
    [Crossref]
  21. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
    [Crossref]
  22. N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89, 015006 (2017).
    [Crossref]
  23. D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, “High-fidelity Rydberg quantum gate via a two-atom dark state,” Phys. Rev. A 96, 042306 (2017).
    [Crossref]
  24. I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018).
    [Crossref]
  25. M. Khazali and K. Mølmer, “Fast multiqubit gates by adiabatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits,” Phys. Rev. X 10, 021054 (2020).
    [Crossref]
  26. M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, “Symmetric Rydberg controlled-Z gates with adiabatic pulses,” Phys. Rev. A 101, 062309 (2020).
    [Crossref]
  27. A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020).
    [Crossref]
  28. C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98, 023002 (2007).
    [Crossref]
  29. T. Pohl and P. R. Berman, “Breaking the dipole blockade: nearly resonant dipole interactions in few-atom systems,” Phys. Rev. Lett. 102, 013004 (2009).
    [Crossref]
  30. J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009).
    [Crossref]
  31. T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104, 013001 (2010).
    [Crossref]
  32. W. Li, C. Ates, and I. Lesanovsky, “Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps,” Phys. Rev. Lett. 110, 213005 (2013).
    [Crossref]
  33. S. Basak, Y. Chougale, and R. Nath, “Periodically driven array of single Rydberg atoms,” Phys. Rev. Lett. 120, 123204 (2018).
    [Crossref]
  34. S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
    [Crossref]
  35. S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, “One-step construction of the multiple-qubit Rydberg controlled-phase gate,” Phys. Rev. A 98, 032306 (2018).
    [Crossref]
  36. J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, “Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45, 1200–1203 (2020).
    [Crossref]
  37. T. H. Xing, X. Wu, and G. F. Xu, “Nonadiabatic holonomic three-qubit controlled gates realized by one-shot implementation,” Phys. Rev. A 101, 012306 (2020).
    [Crossref]
  38. H.-D. Yin, X.-X. Li, G.-C. Wang, and X.-Q. Shao, “One-step implementation of Toffoli gate for neutral atoms based on unconventional Rydberg pumping,” Opt. Express 28, 35576–35587 (2020).
    [Crossref]
  39. J.-L. Wu, J. Song, and S.-L. Su, “Resonant-interaction-induced Rydberg antiblockade and its applications,” Phys. Lett. A 384, 126039 (2020).
    [Crossref]
  40. S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020).
    [Crossref]
  41. M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, “Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms,” J. Phys. Conf. Ser. 264, 012023 (2011).
    [Crossref]
  42. S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, “Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states,” Phys. Rev. A 97, 053803 (2018).
    [Crossref]
  43. E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1983).
    [Crossref]
  44. N. Schuch and J. Siewert, “Natural two-qubit gate for quantum computation using the XY interaction,” Phys. Rev. A 67, 032301 (2003).
    [Crossref]
  45. L. Isenhower, M. Saffman, and K. Mølmer, “Multibit CkNOT quantum gates via Rydberg blockade,” Quantum Inf. Process. 10, 755 (2011).
    [Crossref]
  46. R. J. Spiteri, M. Schmidt, J. Ghosh, E. Zahedinejad, and B. C. Sanders, “Quantum control for high-fidelity multi-qubit gates,” New J. Phys. 20, 113009 (2018).
    [Crossref]
  47. W. Feng and D.-W. Wang, “Quantum Fredkin gate based on synthetic three-body interactions in superconducting circuits,” Phys. Rev. A 101, 062312 (2020).
    [Crossref]
  48. S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, “Single-step implementation of high-fidelity n-bit Toffoli gates,” Phys. Rev. A 101, 022308 (2020).
    [Crossref]
  49. R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
    [Crossref]
  50. W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
    [Crossref]
  51. N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
    [Crossref]
  52. I. L. Chuang and Y. Yamamoto, “Quantum bit regeneration,” Phys. Rev. Lett. 76, 4281–4284 (1996).
    [Crossref]
  53. H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87, 167902 (2001).
    [Crossref]
  54. B. K. Behera, T. Reza, A. Gupta, and P. K. Panigrahi, “Designing quantum router in IBM quantum computer,” Quantum Inf. Process. 18, 328 (2019).
    [Crossref]
  55. H.-Z. Wu, Z.-B. Yang, and S.-B. Zheng, “Quantum state swap for two trapped Rydberg atoms,” Chin. Phys. B 21, 040305 (2012).
    [Crossref]
  56. X.-F. Shi, F. Bariani, and T. A. B. Kennedy, “Entanglement of neutral-atom chains by spin-exchange Rydberg interaction,” Phys. Rev. A 90, 062327 (2014).
    [Crossref]
  57. A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015).
    [Crossref]
  58. M. Gärttner, K. P. Heeg, T. Gasenzer, and J. Evers, “Dynamic formation of Rydberg aggregates at off-resonant excitation,” Phys. Rev. A 88, 043410 (2013).
    [Crossref]
  59. S.-L. Su, Y. Gao, E. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95, 022319 (2017).
    [Crossref]
  60. X.-Y. Zhu, E. Liang, and S.-L. Su, “Rydberg-atom-based controlled arbitrary-phase gate and its applications,” J. Opt. Soc. Am. B 36, 1937–1944 (2019).
    [Crossref]
  61. D. James and J. Jerke, “Effective Hamiltonian theory and its applications in quantum information,” Can. J. Phys. 85, 625–632 (2007).
    [Crossref]
  62. W. Shao, C. Wu, and X.-L. Feng, “Generalized James’ effective Hamiltonian method,” Phys. Rev. A 95, 032124 (2017).
    [Crossref]
  63. M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303, 249–252 (2002).
    [Crossref]
  64. C.-Y. Guo, L.-L. Yan, S. Zhang, S.-L. Su, and W. Li, “Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms,” Phys. Rev. A 102, 042607 (2020).
    [Crossref]
  65. F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
    [Crossref]
  66. E. Brion, L. H. Pedersen, and K. Mølmer, “Implementing a neutral atom Rydberg gate without populating the Rydberg state,” J. Phys. B 40, S159–S166 (2007).
    [Crossref]
  67. J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
    [Crossref]
  68. X.-F. Shi, “Fast, accurate, and realizable two-qubit entangling gates by quantum interference in detuned Rabi cycles of Rydberg atoms,” Phys. Rev. Appl. 11, 044035 (2019).
    [Crossref]
  69. X.-F. Shi, “Suppressing motional dephasing of ground-Rydberg transition for high-fidelity quantum control with neutral atoms,” Phys. Rev. Appl. 13, 024008 (2020).
    [Crossref]
  70. A. G. Fowler, A. M. Stephens, and P. Groszkowski, “High-threshold universal quantum computation on the surface code,” Phys. Rev. A 80, 052312 (2009).
    [Crossref]

2021 (1)

J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
[Crossref]

2020 (17)

C.-Y. Guo, L.-L. Yan, S. Zhang, S.-L. Su, and W. Li, “Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms,” Phys. Rev. A 102, 042607 (2020).
[Crossref]

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

X.-F. Shi, “Suppressing motional dephasing of ground-Rydberg transition for high-fidelity quantum control with neutral atoms,” Phys. Rev. Appl. 13, 024008 (2020).
[Crossref]

J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, “Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45, 1200–1203 (2020).
[Crossref]

T. H. Xing, X. Wu, and G. F. Xu, “Nonadiabatic holonomic three-qubit controlled gates realized by one-shot implementation,” Phys. Rev. A 101, 012306 (2020).
[Crossref]

H.-D. Yin, X.-X. Li, G.-C. Wang, and X.-Q. Shao, “One-step implementation of Toffoli gate for neutral atoms based on unconventional Rydberg pumping,” Opt. Express 28, 35576–35587 (2020).
[Crossref]

J.-L. Wu, J. Song, and S.-L. Su, “Resonant-interaction-induced Rydberg antiblockade and its applications,” Phys. Lett. A 384, 126039 (2020).
[Crossref]

S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020).
[Crossref]

W. Feng and D.-W. Wang, “Quantum Fredkin gate based on synthetic three-body interactions in superconducting circuits,” Phys. Rev. A 101, 062312 (2020).
[Crossref]

S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, “Single-step implementation of high-fidelity n-bit Toffoli gates,” Phys. Rev. A 101, 022308 (2020).
[Crossref]

A. Browaeys and T. Lahaye, “Many-body physics with individually controlled Rydberg atoms,” Nat. Phys. 16, 132–142 (2020).
[Crossref]

Z.-Y. Zhang, T.-Y. Zhang, Z.-K. Liu, D.-S. Ding, and B.-S. Shi, “Research progress of Rydberg many-body interaction,” Acta Phys. Sin. 69, 080301 (2020).
[Crossref]

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

B.-J. Liu, S.-L. Su, and M.-H. Yung, “Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms,” Phys. Rev. Res. 2, 043130 (2020).
[Crossref]

M. Khazali and K. Mølmer, “Fast multiqubit gates by adiabatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits,” Phys. Rev. X 10, 021054 (2020).
[Crossref]

M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, “Symmetric Rydberg controlled-Z gates with adiabatic pulses,” Phys. Rev. A 101, 062309 (2020).
[Crossref]

A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020).
[Crossref]

2019 (10)

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

C.-P. Shen, J.-L. Wu, S.-L. Su, and E. Liang, “Construction of robust Rydberg controlled-phase gates,” Opt. Lett. 44, 2036–2039 (2019).
[Crossref]

K.-Y. Liao, X.-H. Liu, Z. Li, and Y.-X. Du, “Geometric Rydberg quantum gate with shortcuts to adiabaticity,” Opt. Lett. 44, 4801–4804 (2019).
[Crossref]

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

B. K. Behera, T. Reza, A. Gupta, and P. K. Panigrahi, “Designing quantum router in IBM quantum computer,” Quantum Inf. Process. 18, 328 (2019).
[Crossref]

X.-F. Shi, “Fast, accurate, and realizable two-qubit entangling gates by quantum interference in detuned Rabi cycles of Rydberg atoms,” Phys. Rev. Appl. 11, 044035 (2019).
[Crossref]

X.-Y. Zhu, E. Liang, and S.-L. Su, “Rydberg-atom-based controlled arbitrary-phase gate and its applications,” J. Opt. Soc. Am. B 36, 1937–1944 (2019).
[Crossref]

2018 (7)

R. J. Spiteri, M. Schmidt, J. Ghosh, E. Zahedinejad, and B. C. Sanders, “Quantum control for high-fidelity multi-qubit gates,” New J. Phys. 20, 113009 (2018).
[Crossref]

S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, “Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states,” Phys. Rev. A 97, 053803 (2018).
[Crossref]

S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, “One-step construction of the multiple-qubit Rydberg controlled-phase gate,” Phys. Rev. A 98, 032306 (2018).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

X.-F. Shi, “Deutsch, Toffoli, and CNOT gates via Rydberg blockade of neutral atoms,” Phys. Rev. Appl. 9, 051001 (2018).
[Crossref]

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018).
[Crossref]

S. Basak, Y. Chougale, and R. Nath, “Periodically driven array of single Rydberg atoms,” Phys. Rev. Lett. 120, 123204 (2018).
[Crossref]

2017 (5)

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89, 015006 (2017).
[Crossref]

D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, “High-fidelity Rydberg quantum gate via a two-atom dark state,” Phys. Rev. A 96, 042306 (2017).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

W. Shao, C. Wu, and X.-L. Feng, “Generalized James’ effective Hamiltonian method,” Phys. Rev. A 95, 032124 (2017).
[Crossref]

S.-L. Su, Y. Gao, E. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95, 022319 (2017).
[Crossref]

2016 (3)

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

M. Saffman, “Quantum computing with atomic qubits and Rydberg interactions: progress and challenges,” J. Phys. B 49, 202001 (2016).
[Crossref]

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
[Crossref]

2015 (2)

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015).
[Crossref]

2014 (1)

X.-F. Shi, F. Bariani, and T. A. B. Kennedy, “Entanglement of neutral-atom chains by spin-exchange Rydberg interaction,” Phys. Rev. A 90, 062327 (2014).
[Crossref]

2013 (2)

M. Gärttner, K. P. Heeg, T. Gasenzer, and J. Evers, “Dynamic formation of Rydberg aggregates at off-resonant excitation,” Phys. Rev. A 88, 043410 (2013).
[Crossref]

W. Li, C. Ates, and I. Lesanovsky, “Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps,” Phys. Rev. Lett. 110, 213005 (2013).
[Crossref]

2012 (1)

H.-Z. Wu, Z.-B. Yang, and S.-B. Zheng, “Quantum state swap for two trapped Rydberg atoms,” Chin. Phys. B 21, 040305 (2012).
[Crossref]

2011 (3)

L. Isenhower, M. Saffman, and K. Mølmer, “Multibit CkNOT quantum gates via Rydberg blockade,” Quantum Inf. Process. 10, 755 (2011).
[Crossref]

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
[Crossref]

M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, “Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms,” J. Phys. Conf. Ser. 264, 012023 (2011).
[Crossref]

2010 (2)

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104, 013001 (2010).
[Crossref]

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

2009 (5)

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
[Crossref]

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

T. Pohl and P. R. Berman, “Breaking the dipole blockade: nearly resonant dipole interactions in few-atom systems,” Phys. Rev. Lett. 102, 013004 (2009).
[Crossref]

J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009).
[Crossref]

A. G. Fowler, A. M. Stephens, and P. Groszkowski, “High-threshold universal quantum computation on the surface code,” Phys. Rev. A 80, 052312 (2009).
[Crossref]

2007 (3)

E. Brion, L. H. Pedersen, and K. Mølmer, “Implementing a neutral atom Rydberg gate without populating the Rydberg state,” J. Phys. B 40, S159–S166 (2007).
[Crossref]

D. James and J. Jerke, “Effective Hamiltonian theory and its applications in quantum information,” Can. J. Phys. 85, 625–632 (2007).
[Crossref]

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98, 023002 (2007).
[Crossref]

2003 (1)

N. Schuch and J. Siewert, “Natural two-qubit gate for quantum computation using the XY interaction,” Phys. Rev. A 67, 032301 (2003).
[Crossref]

2002 (1)

M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303, 249–252 (2002).
[Crossref]

2001 (2)

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87, 167902 (2001).
[Crossref]

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

2000 (1)

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000).
[Crossref]

1998 (1)

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

1996 (1)

I. L. Chuang and Y. Yamamoto, “Quantum bit regeneration,” Phys. Rev. Lett. 76, 4281–4284 (1996).
[Crossref]

1983 (1)

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1983).
[Crossref]

Amthor, T.

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104, 013001 (2010).
[Crossref]

Arute, F.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Arya, K.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Ates, C.

W. Li, C. Ates, and I. Lesanovsky, “Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps,” Phys. Rev. Lett. 110, 213005 (2013).
[Crossref]

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98, 023002 (2007).
[Crossref]

Barends, R.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Bariani, F.

X.-F. Shi, F. Bariani, and T. A. B. Kennedy, “Entanglement of neutral-atom chains by spin-exchange Rydberg interaction,” Phys. Rev. A 90, 062327 (2014).
[Crossref]

Barredo, D.

S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, “Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states,” Phys. Rev. A 97, 053803 (2018).
[Crossref]

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

Basak, S.

S. Basak, Y. Chougale, and R. Nath, “Periodically driven array of single Rydberg atoms,” Phys. Rev. Lett. 120, 123204 (2018).
[Crossref]

Behera, B. K.

B. K. Behera, T. Reza, A. Gupta, and P. K. Panigrahi, “Designing quantum router in IBM quantum computer,” Quantum Inf. Process. 18, 328 (2019).
[Crossref]

Bergmann, K.

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89, 015006 (2017).
[Crossref]

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

Berman, P. R.

T. Pohl and P. R. Berman, “Breaking the dipole blockade: nearly resonant dipole interactions in few-atom systems,” Phys. Rev. Lett. 102, 013004 (2009).
[Crossref]

Bernien, H.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Beterov, I. I.

M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, “Symmetric Rydberg controlled-Z gates with adiabatic pulses,” Phys. Rev. A 101, 062309 (2020).
[Crossref]

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018).
[Crossref]

Biedermann, G. W.

A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020).
[Crossref]

Bloch, I.

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015).
[Crossref]

Boixo, S.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Brion, E.

E. Brion, L. H. Pedersen, and K. Mølmer, “Implementing a neutral atom Rydberg gate without populating the Rydberg state,” J. Phys. B 40, S159–S166 (2007).
[Crossref]

Browaeys, A.

A. Browaeys and T. Lahaye, “Many-body physics with individually controlled Rydberg atoms,” Nat. Phys. 16, 132–142 (2020).
[Crossref]

S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, “Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states,” Phys. Rev. A 97, 053803 (2018).
[Crossref]

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Buell, D.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Buhrman, H.

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87, 167902 (2001).
[Crossref]

Burkett, B.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Calarco, T.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

Chen, Y.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Chen, Z.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Cheneau, M.

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

Chiaro, B.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Choi, J.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

Choi, S.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Chotia, A.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Chougale, Y.

S. Basak, Y. Chougale, and R. Nath, “Periodically driven array of single Rydberg atoms,” Phys. Rev. Lett. 120, 123204 (2018).
[Crossref]

Chuang, I. L.

I. L. Chuang and Y. Yamamoto, “Quantum bit regeneration,” Phys. Rev. Lett. 76, 4281–4284 (1996).
[Crossref]

Cirac, J. I.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000).
[Crossref]

Cleve, R.

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87, 167902 (2001).
[Crossref]

Collins, R.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Comparat, D.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Cooper, A.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

Cote, R.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

Côté, R.

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000).
[Crossref]

Covey, J. P.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

Cui, J.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

Dalal, A.

M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, “Symmetric Rydberg controlled-Z gates with adiabatic pulses,” Phys. Rev. A 101, 062309 (2020).
[Crossref]

Dalmonte, M.

A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015).
[Crossref]

de Léséleuc, S.

S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, “Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states,” Phys. Rev. A 97, 053803 (2018).
[Crossref]

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

de Riedmatten, H.

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
[Crossref]

de Wolf, R.

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87, 167902 (2001).
[Crossref]

Deng, H.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

Deutsch, I. H.

A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020).
[Crossref]

Ding, D.-S.

Z.-Y. Zhang, T.-Y. Zhang, Z.-K. Liu, D.-S. Ding, and B.-S. Shi, “Research progress of Rydberg many-body interaction,” Acta Phys. Sin. 69, 080301 (2020).
[Crossref]

Du, Y.-X.

Duan, L. M.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

Dunsworth, A.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Ebadi, S.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

Ebert, M.

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

Endres, M.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Entin, V. M.

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018).
[Crossref]

Evers, J.

M. Gärttner, K. P. Heeg, T. Gasenzer, and J. Evers, “Dynamic formation of Rydberg aggregates at off-resonant excitation,” Phys. Rev. A 88, 043410 (2013).
[Crossref]

Feng, M.

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

Feng, W.

W. Feng and D.-W. Wang, “Quantum Fredkin gate based on synthetic three-body interactions in superconducting circuits,” Phys. Rev. A 101, 062312 (2020).
[Crossref]

Feng, X.-L.

W. Shao, C. Wu, and X.-L. Feng, “Generalized James’ effective Hamiltonian method,” Phys. Rev. A 95, 032124 (2017).
[Crossref]

J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009).
[Crossref]

Fleischhauer, M.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

Fowler, A.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Fowler, A. G.

A. G. Fowler, A. M. Stephens, and P. Groszkowski, “High-threshold universal quantum computation on the surface code,” Phys. Rev. A 80, 052312 (2009).
[Crossref]

Foxen, B.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Fredkin, E.

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1983).
[Crossref]

Fukuhara, T.

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

Gaëtan, A.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Gao, Y.

S.-L. Su, Y. Gao, E. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95, 022319 (2017).
[Crossref]

Gärttner, M.

M. Gärttner, K. P. Heeg, T. Gasenzer, and J. Evers, “Dynamic formation of Rydberg aggregates at off-resonant excitation,” Phys. Rev. A 88, 043410 (2013).
[Crossref]

Gasenzer, T.

M. Gärttner, K. P. Heeg, T. Gasenzer, and J. Evers, “Dynamic formation of Rydberg aggregates at off-resonant excitation,” Phys. Rev. A 88, 043410 (2013).
[Crossref]

Gerritsma, R.

S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, “Single-step implementation of high-fidelity n-bit Toffoli gates,” Phys. Rev. A 101, 022308 (2020).
[Crossref]

Ghosh, J.

R. J. Spiteri, M. Schmidt, J. Ghosh, E. Zahedinejad, and B. C. Sanders, “Quantum control for high-fidelity multi-qubit gates,” New J. Phys. 20, 113009 (2018).
[Crossref]

Gidney, C.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Giese, C.

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104, 013001 (2010).
[Crossref]

Gill, A. T.

M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, “Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms,” J. Phys. Conf. Ser. 264, 012023 (2011).
[Crossref]

Gisin, N.

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
[Crossref]

Giustina, M.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Glaetzle, A. W.

A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015).
[Crossref]

Graff, R.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Graham, T. M.

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

Grangier, P.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Greiner, M.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Grinkemeyer, B.

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

Groenland, K.

S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, “Single-step implementation of high-fidelity n-bit Toffoli gates,” Phys. Rev. A 101, 022308 (2020).
[Crossref]

Gross, C.

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015).
[Crossref]

Groszkowski, P.

A. G. Fowler, A. M. Stephens, and P. Groszkowski, “High-threshold universal quantum computation on the surface code,” Phys. Rev. A 80, 052312 (2009).
[Crossref]

Guo, C.-Y.

C.-Y. Guo, L.-L. Yan, S. Zhang, S.-L. Su, and W. Li, “Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms,” Phys. Rev. A 102, 042607 (2020).
[Crossref]

Guo, F.-Q.

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020).
[Crossref]

Gupta, A.

B. K. Behera, T. Reza, A. Gupta, and P. K. Panigrahi, “Designing quantum router in IBM quantum computer,” Quantum Inf. Process. 18, 328 (2019).
[Crossref]

Hamzina, G. N.

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018).
[Crossref]

Han, J.-X.

J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
[Crossref]

Han, P.-R.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

Heeg, K. P.

M. Gärttner, K. P. Heeg, T. Gasenzer, and J. Evers, “Dynamic formation of Rydberg aggregates at off-resonant excitation,” Phys. Rev. A 88, 043410 (2013).
[Crossref]

Henage, T.

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
[Crossref]

Hild, S.

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

Hofmann, C. S.

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104, 013001 (2010).
[Crossref]

Huang, T.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Huang, X.-J.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

Isenhower, L.

M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, “Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms,” J. Phys. Conf. Ser. 264, 012023 (2011).
[Crossref]

L. Isenhower, M. Saffman, and K. Mølmer, “Multibit CkNOT quantum gates via Rydberg blockade,” Quantum Inf. Process. 10, 755 (2011).
[Crossref]

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
[Crossref]

Jaksch, D.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000).
[Crossref]

James, D.

D. James and J. Jerke, “Effective Hamiltonian theory and its applications in quantum information,” Can. J. Phys. 85, 625–632 (2007).
[Crossref]

Jeffrey, E.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Jerke, J.

D. James and J. Jerke, “Effective Hamiltonian theory and its applications in quantum information,” Can. J. Phys. 85, 625–632 (2007).
[Crossref]

Jiang, X.

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

Jiang, Y.

J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
[Crossref]

J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, “Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45, 1200–1203 (2020).
[Crossref]

Jin, Z.

S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020).
[Crossref]

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
[Crossref]

Johnson, T. A.

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
[Crossref]

Kafri, D.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Kale, A.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

Ke, M.

J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009).
[Crossref]

Kechedzhi, K.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Keesling, A.

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Kelly, J.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Kennedy, T. A. B.

X.-F. Shi, F. Bariani, and T. A. B. Kennedy, “Entanglement of neutral-atom chains by spin-exchange Rydberg interaction,” Phys. Rev. A 90, 062327 (2014).
[Crossref]

Khazali, M.

M. Khazali and K. Mølmer, “Fast multiqubit gates by adiabatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits,” Phys. Rev. X 10, 021054 (2020).
[Crossref]

Klimov, P. V.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Kostritsa, F.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Kwon, M.

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

Labuhn, H.

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

Lahaye, T.

A. Browaeys and T. Lahaye, “Many-body physics with individually controlled Rydberg atoms,” Nat. Phys. 16, 132–142 (2020).
[Crossref]

S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, “Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states,” Phys. Rev. A 97, 053803 (2018).
[Crossref]

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

Landhuis, D.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Lesanovsky, I.

W. Li, C. Ates, and I. Lesanovsky, “Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps,” Phys. Rev. Lett. 110, 213005 (2013).
[Crossref]

Levine, H.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Li, H.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

Li, W.

C.-Y. Guo, L.-L. Yan, S. Zhang, S.-L. Su, and W. Li, “Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms,” Phys. Rev. A 102, 042607 (2020).
[Crossref]

W. Li, C. Ates, and I. Lesanovsky, “Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps,” Phys. Rev. Lett. 110, 213005 (2013).
[Crossref]

Li, X.-X.

Li, Z.

Liang, E.

C.-P. Shen, J.-L. Wu, S.-L. Su, and E. Liang, “Construction of robust Rydberg controlled-phase gates,” Opt. Lett. 44, 2036–2039 (2019).
[Crossref]

X.-Y. Zhu, E. Liang, and S.-L. Su, “Rydberg-atom-based controlled arbitrary-phase gate and its applications,” J. Opt. Soc. Am. B 36, 1937–1944 (2019).
[Crossref]

S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, “One-step construction of the multiple-qubit Rydberg controlled-phase gate,” Phys. Rev. A 98, 032306 (2018).
[Crossref]

S.-L. Su, Y. Gao, E. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95, 022319 (2017).
[Crossref]

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
[Crossref]

Liao, K.-Y.

Lichtman, M. T.

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

Lienhard, V.

S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, “Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states,” Phys. Rev. A 97, 053803 (2018).
[Crossref]

Liu, B.-J.

B.-J. Liu, S.-L. Su, and M.-H. Yung, “Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms,” Phys. Rev. Res. 2, 043130 (2020).
[Crossref]

Liu, X.-H.

Liu, Z.-K.

Z.-Y. Zhang, T.-Y. Zhang, Z.-K. Liu, D.-S. Ding, and B.-S. Shi, “Research progress of Rydberg many-body interaction,” Acta Phys. Sin. 69, 080301 (2020).
[Crossref]

Lucero, E.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Lukin, M. D.

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000).
[Crossref]

Macr, T.

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

Macrì, T.

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

Madjarov, I. S.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

Marino, A. M.

A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020).
[Crossref]

Marra, Z.

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

Martin, M. J.

A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020).
[Crossref]

Martinis, J. M.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

McEwen, M.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Megrant, A.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Mi, X.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Miroshnychenko, Y.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Mitra, A.

A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020).
[Crossref]

Mølmer, K.

M. Khazali and K. Mølmer, “Fast multiqubit gates by adiabatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits,” Phys. Rev. X 10, 021054 (2020).
[Crossref]

D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, “High-fidelity Rydberg quantum gate via a two-atom dark state,” Phys. Rev. A 96, 042306 (2017).
[Crossref]

L. Isenhower, M. Saffman, and K. Mølmer, “Multibit CkNOT quantum gates via Rydberg blockade,” Quantum Inf. Process. 10, 755 (2011).
[Crossref]

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

E. Brion, L. H. Pedersen, and K. Mølmer, “Implementing a neutral atom Rydberg gate without populating the Rydberg state,” J. Phys. B 40, S159–S166 (2007).
[Crossref]

Montangero, S.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

Motzoi, F.

D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, “High-fidelity Rydberg quantum gate via a two-atom dark state,” Phys. Rev. A 96, 042306 (2017).
[Crossref]

Mutus, J.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Naaman, O.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Nath, R.

S. Basak, Y. Chougale, and R. Nath, “Periodically driven array of single Rydberg atoms,” Phys. Rev. Lett. 120, 123204 (2018).
[Crossref]

A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015).
[Crossref]

Neeley, M.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Neill, C.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Neven, H.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Nielsen, M. A.

M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303, 249–252 (2002).
[Crossref]

Ning, W.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

Oh, C. H.

J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009).
[Crossref]

Omran, A.

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Ostby, E.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Páez, E. J.

M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, “Symmetric Rydberg controlled-Z gates with adiabatic pulses,” Phys. Rev. A 101, 062309 (2020).
[Crossref]

Panigrahi, P. K.

B. K. Behera, T. Reza, A. Gupta, and P. K. Panigrahi, “Designing quantum router in IBM quantum computer,” Quantum Inf. Process. 18, 328 (2019).
[Crossref]

Pattard, T.

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98, 023002 (2007).
[Crossref]

Pedersen, L. H.

E. Brion, L. H. Pedersen, and K. Mølmer, “Implementing a neutral atom Rydberg gate without populating the Rydberg state,” J. Phys. B 40, S159–S166 (2007).
[Crossref]

Petrosyan, D.

D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, “High-fidelity Rydberg quantum gate via a two-atom dark state,” Phys. Rev. A 96, 042306 (2017).
[Crossref]

Petukhov, A. G.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Pichler, H.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Pillet, P.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Poggi, P. M.

A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020).
[Crossref]

Pohl, T.

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

T. Pohl and P. R. Berman, “Breaking the dipole blockade: nearly resonant dipole interactions in few-atom systems,” Phys. Rev. Lett. 102, 013004 (2009).
[Crossref]

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98, 023002 (2007).
[Crossref]

Qian, J.

J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009).
[Crossref]

Qian, Y.

J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009).
[Crossref]

Quintana, C. M.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Rangelov, A. A.

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89, 015006 (2017).
[Crossref]

Rasmussen, S. E.

S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, “Single-step implementation of high-fidelity n-bit Toffoli gates,” Phys. Rev. A 101, 022308 (2020).
[Crossref]

Ravets, S.

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

Rembold, P.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

Reza, T.

B. K. Behera, T. Reza, A. Gupta, and P. K. Panigrahi, “Designing quantum router in IBM quantum computer,” Quantum Inf. Process. 18, 328 (2019).
[Crossref]

Rolston, S. L.

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000).
[Crossref]

Rossignolo, M.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

Rost, J. M.

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98, 023002 (2007).
[Crossref]

Roushan, P.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Ryabtsev, I. I.

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018).
[Crossref]

Saffman, M.

M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, “Symmetric Rydberg controlled-Z gates with adiabatic pulses,” Phys. Rev. A 101, 062309 (2020).
[Crossref]

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, “High-fidelity Rydberg quantum gate via a two-atom dark state,” Phys. Rev. A 96, 042306 (2017).
[Crossref]

M. Saffman, “Quantum computing with atomic qubits and Rydberg interactions: progress and challenges,” J. Phys. B 49, 202001 (2016).
[Crossref]

L. Isenhower, M. Saffman, and K. Mølmer, “Multibit CkNOT quantum gates via Rydberg blockade,” Quantum Inf. Process. 10, 755 (2011).
[Crossref]

M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, “Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms,” J. Phys. Conf. Ser. 264, 012023 (2011).
[Crossref]

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
[Crossref]

Sanders, B. C.

M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, “Symmetric Rydberg controlled-Z gates with adiabatic pulses,” Phys. Rev. A 101, 062309 (2020).
[Crossref]

R. J. Spiteri, M. Schmidt, J. Ghosh, E. Zahedinejad, and B. C. Sanders, “Quantum control for high-fidelity multi-qubit gates,” New J. Phys. 20, 113009 (2018).
[Crossref]

Sangouard, N.

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
[Crossref]

Sank, D.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Satzinger, K. J.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Schau, P.

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

Schkolnik, V.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

Schmidt, M.

R. J. Spiteri, M. Schmidt, J. Ghosh, E. Zahedinejad, and B. C. Sanders, “Quantum control for high-fidelity multi-qubit gates,” New J. Phys. 20, 113009 (2018).
[Crossref]

Schoutens, K.

S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, “Single-step implementation of high-fidelity n-bit Toffoli gates,” Phys. Rev. A 101, 022308 (2020).
[Crossref]

Schuch, N.

N. Schuch and J. Siewert, “Natural two-qubit gate for quantum computation using the XY interaction,” Phys. Rev. A 67, 032301 (2003).
[Crossref]

Schwartz, S.

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Semeghini, G.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

Shao, W.

W. Shao, C. Wu, and X.-L. Feng, “Generalized James’ effective Hamiltonian method,” Phys. Rev. A 95, 032124 (2017).
[Crossref]

Shao, X. Q.

S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020).
[Crossref]

Shao, X.-Q.

Shaw, A. L.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

Shen, C.-P.

Shen, H. Z.

S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, “One-step construction of the multiple-qubit Rydberg controlled-phase gate,” Phys. Rev. A 98, 032306 (2018).
[Crossref]

Shi, B.-S.

Z.-Y. Zhang, T.-Y. Zhang, Z.-K. Liu, D.-S. Ding, and B.-S. Shi, “Research progress of Rydberg many-body interaction,” Acta Phys. Sin. 69, 080301 (2020).
[Crossref]

Shi, X.-F.

X.-F. Shi, “Suppressing motional dephasing of ground-Rydberg transition for high-fidelity quantum control with neutral atoms,” Phys. Rev. Appl. 13, 024008 (2020).
[Crossref]

X.-F. Shi, “Fast, accurate, and realizable two-qubit entangling gates by quantum interference in detuned Rabi cycles of Rydberg atoms,” Phys. Rev. Appl. 11, 044035 (2019).
[Crossref]

X.-F. Shi, “Deutsch, Toffoli, and CNOT gates via Rydberg blockade of neutral atoms,” Phys. Rev. Appl. 9, 051001 (2018).
[Crossref]

X.-F. Shi, F. Bariani, and T. A. B. Kennedy, “Entanglement of neutral-atom chains by spin-exchange Rydberg interaction,” Phys. Rev. A 90, 062327 (2014).
[Crossref]

Shore, B. W.

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89, 015006 (2017).
[Crossref]

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

Siewert, J.

N. Schuch and J. Siewert, “Natural two-qubit gate for quantum computation using the XY interaction,” Phys. Rev. A 67, 032301 (2003).
[Crossref]

Simon, C.

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
[Crossref]

Smelyanskiy, V. N.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Song, J.

J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
[Crossref]

J.-L. Wu, J. Song, and S.-L. Su, “Resonant-interaction-induced Rydberg antiblockade and its applications,” Phys. Lett. A 384, 126039 (2020).
[Crossref]

J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, “Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45, 1200–1203 (2020).
[Crossref]

Spiteri, R. J.

R. J. Spiteri, M. Schmidt, J. Ghosh, E. Zahedinejad, and B. C. Sanders, “Quantum control for high-fidelity multi-qubit gates,” New J. Phys. 20, 113009 (2018).
[Crossref]

Stephens, A. M.

A. G. Fowler, A. M. Stephens, and P. Groszkowski, “High-threshold universal quantum computation on the surface code,” Phys. Rev. A 80, 052312 (2009).
[Crossref]

Su, S. L.

S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, “One-step construction of the multiple-qubit Rydberg controlled-phase gate,” Phys. Rev. A 98, 032306 (2018).
[Crossref]

Su, S.-L.

J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
[Crossref]

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

C.-Y. Guo, L.-L. Yan, S. Zhang, S.-L. Su, and W. Li, “Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms,” Phys. Rev. A 102, 042607 (2020).
[Crossref]

J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, “Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45, 1200–1203 (2020).
[Crossref]

J.-L. Wu, J. Song, and S.-L. Su, “Resonant-interaction-induced Rydberg antiblockade and its applications,” Phys. Lett. A 384, 126039 (2020).
[Crossref]

S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020).
[Crossref]

B.-J. Liu, S.-L. Su, and M.-H. Yung, “Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms,” Phys. Rev. Res. 2, 043130 (2020).
[Crossref]

C.-P. Shen, J.-L. Wu, S.-L. Su, and E. Liang, “Construction of robust Rydberg controlled-phase gates,” Opt. Lett. 44, 2036–2039 (2019).
[Crossref]

X.-Y. Zhu, E. Liang, and S.-L. Su, “Rydberg-atom-based controlled arbitrary-phase gate and its applications,” J. Opt. Soc. Am. B 36, 1937–1944 (2019).
[Crossref]

S.-L. Su, Y. Gao, E. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95, 022319 (2017).
[Crossref]

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
[Crossref]

Sun, L.-L.

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
[Crossref]

Sun, Y.

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

Theuer, H.

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

Toffoli, T.

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1983).
[Crossref]

Tretyakov, D. B.

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018).
[Crossref]

Urban, E.

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
[Crossref]

Vainsencher, A.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Vitanov, N. V.

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89, 015006 (2017).
[Crossref]

Viteau, M.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Vuletic, V.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Walker, T. G.

M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, “Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms,” J. Phys. Conf. Ser. 264, 012023 (2011).
[Crossref]

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
[Crossref]

Wang, D.-W.

W. Feng and D.-W. Wang, “Quantum Fredkin gate based on synthetic three-body interactions in superconducting circuits,” Phys. Rev. A 101, 062312 (2020).
[Crossref]

Wang, G.-C.

Wang, T. T.

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

Wang, Y.

J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
[Crossref]

J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, “Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45, 1200–1203 (2020).
[Crossref]

J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009).
[Crossref]

Watrous, J.

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87, 167902 (2001).
[Crossref]

Weidemüller, M.

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104, 013001 (2010).
[Crossref]

Wen, J.-J.

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
[Crossref]

White, T.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Wilk, T.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Williams, J. R.

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

Wu, C.

W. Shao, C. Wu, and X.-L. Feng, “Generalized James’ effective Hamiltonian method,” Phys. Rev. A 95, 032124 (2017).
[Crossref]

Wu, H.-Z.

H.-Z. Wu, Z.-B. Yang, and S.-B. Zheng, “Quantum state swap for two trapped Rydberg atoms,” Chin. Phys. B 21, 040305 (2012).
[Crossref]

Wu, J.-L.

J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
[Crossref]

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

J.-L. Wu, J. Song, and S.-L. Su, “Resonant-interaction-induced Rydberg antiblockade and its applications,” Phys. Lett. A 384, 126039 (2020).
[Crossref]

S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020).
[Crossref]

J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, “Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45, 1200–1203 (2020).
[Crossref]

C.-P. Shen, J.-L. Wu, S.-L. Su, and E. Liang, “Construction of robust Rydberg controlled-phase gates,” Opt. Lett. 44, 2036–2039 (2019).
[Crossref]

Wu, X.

T. H. Xing, X. Wu, and G. F. Xu, “Nonadiabatic holonomic three-qubit controlled gates realized by one-shot implementation,” Phys. Rev. A 101, 012306 (2020).
[Crossref]

Xia, Y.

J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
[Crossref]

J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, “Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45, 1200–1203 (2020).
[Crossref]

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

Xing, T. H.

T. H. Xing, X. Wu, and G. F. Xu, “Nonadiabatic holonomic three-qubit controlled gates realized by one-shot implementation,” Phys. Rev. A 101, 012306 (2020).
[Crossref]

Xu, G. F.

T. H. Xing, X. Wu, and G. F. Xu, “Nonadiabatic holonomic three-qubit controlled gates realized by one-shot implementation,” Phys. Rev. A 101, 012306 (2020).
[Crossref]

Xu, K.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

Yakshina, E. A.

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018).
[Crossref]

Yamamoto, Y.

I. L. Chuang and Y. Yamamoto, “Quantum bit regeneration,” Phys. Rev. Lett. 76, 4281–4284 (1996).
[Crossref]

Yan, L.-L.

C.-Y. Guo, L.-L. Yan, S. Zhang, S.-L. Su, and W. Li, “Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms,” Phys. Rev. A 102, 042607 (2020).
[Crossref]

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

Yang, Z.-B.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

H.-Z. Wu, Z.-B. Yang, and S.-B. Zheng, “Quantum state swap for two trapped Rydberg atoms,” Chin. Phys. B 21, 040305 (2012).
[Crossref]

Yao, J.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Yavuz, D. D.

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
[Crossref]

Yeh, P.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Yin, H.-D.

Yung, M.-H.

B.-J. Liu, S.-L. Su, and M.-H. Yung, “Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms,” Phys. Rev. Res. 2, 043130 (2020).
[Crossref]

Zahedinejad, E.

R. J. Spiteri, M. Schmidt, J. Ghosh, E. Zahedinejad, and B. C. Sanders, “Quantum control for high-fidelity multi-qubit gates,” New J. Phys. 20, 113009 (2018).
[Crossref]

Zalcman, A.

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

Zeiher, J.

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

Zeng, Y.

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

Zhang, S.

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

C.-Y. Guo, L.-L. Yan, S. Zhang, S.-L. Su, and W. Li, “Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms,” Phys. Rev. A 102, 042607 (2020).
[Crossref]

S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020).
[Crossref]

S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, “One-step construction of the multiple-qubit Rydberg controlled-phase gate,” Phys. Rev. A 98, 032306 (2018).
[Crossref]

S.-L. Su, Y. Gao, E. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95, 022319 (2017).
[Crossref]

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
[Crossref]

Zhang, T.-Y.

Z.-Y. Zhang, T.-Y. Zhang, Z.-K. Liu, D.-S. Ding, and B.-S. Shi, “Research progress of Rydberg many-body interaction,” Acta Phys. Sin. 69, 080301 (2020).
[Crossref]

Zhang, X. L.

M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, “Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms,” J. Phys. Conf. Ser. 264, 012023 (2011).
[Crossref]

Zhang, Z.-Y.

Z.-Y. Zhang, T.-Y. Zhang, Z.-K. Liu, D.-S. Ding, and B.-S. Shi, “Research progress of Rydberg many-body interaction,” Acta Phys. Sin. 69, 080301 (2020).
[Crossref]

Zheng, D.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

Zheng, S.-B.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

H.-Z. Wu, Z.-B. Yang, and S.-B. Zheng, “Quantum state swap for two trapped Rydberg atoms,” Chin. Phys. B 21, 040305 (2012).
[Crossref]

Zhong, Z.-R.

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

Zhu, A.-D.

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
[Crossref]

Zhu, X.-Y.

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

X.-Y. Zhu, E. Liang, and S.-L. Su, “Rydberg-atom-based controlled arbitrary-phase gate and its applications,” J. Opt. Soc. Am. B 36, 1937–1944 (2019).
[Crossref]

Zibrov, A. S.

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

Zinner, N. T.

S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, “Single-step implementation of high-fidelity n-bit Toffoli gates,” Phys. Rev. A 101, 022308 (2020).
[Crossref]

Zoller, P.

A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015).
[Crossref]

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000).
[Crossref]

Acta Phys. Sin. (1)

Z.-Y. Zhang, T.-Y. Zhang, Z.-K. Liu, D.-S. Ding, and B.-S. Shi, “Research progress of Rydberg many-body interaction,” Acta Phys. Sin. 69, 080301 (2020).
[Crossref]

Can. J. Phys. (1)

D. James and J. Jerke, “Effective Hamiltonian theory and its applications in quantum information,” Can. J. Phys. 85, 625–632 (2007).
[Crossref]

Chin. Phys. B (1)

H.-Z. Wu, Z.-B. Yang, and S.-B. Zheng, “Quantum state swap for two trapped Rydberg atoms,” Chin. Phys. B 21, 040305 (2012).
[Crossref]

Europhys. Lett. (1)

S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, “Rydberg antiblockade regimes: dynamics and applications,” Europhys. Lett. 131, 53001 (2020).
[Crossref]

Int. J. Theor. Phys. (1)

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1983).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. B (2)

E. Brion, L. H. Pedersen, and K. Mølmer, “Implementing a neutral atom Rydberg gate without populating the Rydberg state,” J. Phys. B 40, S159–S166 (2007).
[Crossref]

M. Saffman, “Quantum computing with atomic qubits and Rydberg interactions: progress and challenges,” J. Phys. B 49, 202001 (2016).
[Crossref]

J. Phys. Conf. Ser. (1)

M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, “Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms,” J. Phys. Conf. Ser. 264, 012023 (2011).
[Crossref]

Nat. Phys. (4)

A. Browaeys and T. Lahaye, “Many-body physics with individually controlled Rydberg atoms,” Nat. Phys. 16, 132–142 (2020).
[Crossref]

I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, “High-fidelity entanglement and detection of alkaline-earth Rydberg atoms,” Nat. Phys. 16, 857–861 (2020).
[Crossref]

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5, 110–114 (2009).
[Crossref]

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the Rydberg blockade regime,” Nat. Phys. 5, 115–118 (2009).
[Crossref]

Nature (2)

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref]

New J. Phys. (1)

R. J. Spiteri, M. Schmidt, J. Ghosh, E. Zahedinejad, and B. C. Sanders, “Quantum control for high-fidelity multi-qubit gates,” New J. Phys. 20, 113009 (2018).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Lett. A (2)

J.-L. Wu, J. Song, and S.-L. Su, “Resonant-interaction-induced Rydberg antiblockade and its applications,” Phys. Lett. A 384, 126039 (2020).
[Crossref]

M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303, 249–252 (2002).
[Crossref]

Phys. Rev. A (20)

C.-Y. Guo, L.-L. Yan, S. Zhang, S.-L. Su, and W. Li, “Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms,” Phys. Rev. A 102, 042607 (2020).
[Crossref]

F.-Q. Guo, J.-L. Wu, X.-Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L.-L. Yan, M. Feng, and S.-L. Su, “Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations,” Phys. Rev. A 102, 062410 (2020).
[Crossref]

W. Shao, C. Wu, and X.-L. Feng, “Generalized James’ effective Hamiltonian method,” Phys. Rev. A 95, 032124 (2017).
[Crossref]

J.-L. Wu, Y. Wang, J.-X. Han, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, “Resilient quantum gates on periodically driven Rydberg atoms,” Phys. Rev. A 103, 012601 (2021).
[Crossref]

A. G. Fowler, A. M. Stephens, and P. Groszkowski, “High-threshold universal quantum computation on the surface code,” Phys. Rev. A 80, 052312 (2009).
[Crossref]

W. Feng and D.-W. Wang, “Quantum Fredkin gate based on synthetic three-body interactions in superconducting circuits,” Phys. Rev. A 101, 062312 (2020).
[Crossref]

S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, “Single-step implementation of high-fidelity n-bit Toffoli gates,” Phys. Rev. A 101, 022308 (2020).
[Crossref]

S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, “Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states,” Phys. Rev. A 97, 053803 (2018).
[Crossref]

N. Schuch and J. Siewert, “Natural two-qubit gate for quantum computation using the XY interaction,” Phys. Rev. A 67, 032301 (2003).
[Crossref]

M. Gärttner, K. P. Heeg, T. Gasenzer, and J. Evers, “Dynamic formation of Rydberg aggregates at off-resonant excitation,” Phys. Rev. A 88, 043410 (2013).
[Crossref]

S.-L. Su, Y. Gao, E. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95, 022319 (2017).
[Crossref]

X.-F. Shi, F. Bariani, and T. A. B. Kennedy, “Entanglement of neutral-atom chains by spin-exchange Rydberg interaction,” Phys. Rev. A 90, 062327 (2014).
[Crossref]

T. H. Xing, X. Wu, and G. F. Xu, “Nonadiabatic holonomic three-qubit controlled gates realized by one-shot implementation,” Phys. Rev. A 101, 012306 (2020).
[Crossref]

D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, “High-fidelity Rydberg quantum gate via a two-atom dark state,” Phys. Rev. A 96, 042306 (2017).
[Crossref]

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97, 032701 (2018).
[Crossref]

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93, 012306 (2016).
[Crossref]

S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, “One-step construction of the multiple-qubit Rydberg controlled-phase gate,” Phys. Rev. A 98, 032306 (2018).
[Crossref]

M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, “Symmetric Rydberg controlled-Z gates with adiabatic pulses,” Phys. Rev. A 101, 062309 (2020).
[Crossref]

A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, “Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing,” Phys. Rev. A 101, 030301 (2020).
[Crossref]

J. Qian, Y. Qian, M. Ke, X.-L. Feng, C. H. Oh, and Y. Wang, “Breakdown of the dipole blockade with a zero-area phase-jump pulse,” Phys. Rev. A 80, 053413 (2009).
[Crossref]

Phys. Rev. Appl. (3)

X.-F. Shi, “Deutsch, Toffoli, and CNOT gates via Rydberg blockade of neutral atoms,” Phys. Rev. Appl. 9, 051001 (2018).
[Crossref]

X.-F. Shi, “Fast, accurate, and realizable two-qubit entangling gates by quantum interference in detuned Rabi cycles of Rydberg atoms,” Phys. Rev. Appl. 11, 044035 (2019).
[Crossref]

X.-F. Shi, “Suppressing motional dephasing of ground-Rydberg transition for high-fidelity quantum control with neutral atoms,” Phys. Rev. Appl. 13, 024008 (2020).
[Crossref]

Phys. Rev. Lett. (15)

A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, “Designing frustrated quantum magnets with laser-dressed Rydberg atoms,” Phys. Rev. Lett. 114, 173002 (2015).
[Crossref]

I. L. Chuang and Y. Yamamoto, “Quantum bit regeneration,” Phys. Rev. Lett. 76, 4281–4284 (1996).
[Crossref]

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87, 167902 (2001).
[Crossref]

R. Barends, C. M. Quintana, A. G. Petukhov, Y. Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and J. M. Martinis, “Diabatic gates for frequency-tunable superconducting qubits,” Phys. Rev. Lett. 123, 210501 (2019).
[Crossref]

W. Ning, X.-J. Huang, P.-R. Han, H. Li, H. Deng, Z.-B. Yang, Z.-R. Zhong, Y. Xia, K. Xu, D. Zheng, and S.-B. Zheng, “Deterministic entanglement swapping in a superconducting circuit,” Phys. Rev. Lett. 123, 060502 (2019).
[Crossref]

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85, 2208–2211 (2000).
[Crossref]

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[Crossref]

H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “High-fidelity control and entanglement of Rydberg-atom qubits,” Phys. Rev. Lett. 121, 123603 (2018).
[Crossref]

T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, “Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array,” Phys. Rev. Lett. 123, 230501 (2019).
[Crossref]

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, “Parallel implementation of high-fidelity multiqubit gates with neutral atoms,” Phys. Rev. Lett. 123, 170503 (2019).
[Crossref]

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104, 013001 (2010).
[Crossref]

W. Li, C. Ates, and I. Lesanovsky, “Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps,” Phys. Rev. Lett. 110, 213005 (2013).
[Crossref]

S. Basak, Y. Chougale, and R. Nath, “Periodically driven array of single Rydberg atoms,” Phys. Rev. Lett. 120, 123204 (2018).
[Crossref]

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98, 023002 (2007).
[Crossref]

T. Pohl and P. R. Berman, “Breaking the dipole blockade: nearly resonant dipole interactions in few-atom systems,” Phys. Rev. Lett. 102, 013004 (2009).
[Crossref]

Phys. Rev. Res. (1)

B.-J. Liu, S.-L. Su, and M.-H. Yung, “Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms,” Phys. Rev. Res. 2, 043130 (2020).
[Crossref]

Phys. Rev. X (1)

M. Khazali and K. Mølmer, “Fast multiqubit gates by adiabatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits,” Phys. Rev. X 10, 021054 (2020).
[Crossref]

Quantum Inf. Process. (2)

L. Isenhower, M. Saffman, and K. Mølmer, “Multibit CkNOT quantum gates via Rydberg blockade,” Quantum Inf. Process. 10, 755 (2011).
[Crossref]

B. K. Behera, T. Reza, A. Gupta, and P. K. Panigrahi, “Designing quantum router in IBM quantum computer,” Quantum Inf. Process. 18, 328 (2019).
[Crossref]

Rev. Mod. Phys. (4)

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[Crossref]

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011).
[Crossref]

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, “Stimulated Raman adiabatic passage in physics, chemistry, and beyond,” Rev. Mod. Phys. 89, 015006 (2017).
[Crossref]

Science (2)

P. Schau, ß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macr, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).
[Crossref]

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Generation and manipulation of Schrödinger cat states in Rydberg atom arrays,” Science 365, 570–574 (2019).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. (a) Schematic for implementing a SWAP gate. Two identical atoms are driven resonantly by two AM laser fields, excited from two ground (computational) states |0 and |1 to a Rydberg (mediated) state |r, respectively, with modulated Rabi frequencies Ω0(t) and Ω1(t). Two atoms are coupled to each other by RRI with strength V=C6/d6, C6 being the van der Waals coefficient and d the interatomic distance. The effective Λ-type RAB dynamics is shown in the shadow of (b). (b) Schematic for implementing a CSWAP gate. Inset circle: the control atom c is coupled to target atoms 1 and 2 described in (a), with RRI strengths V1c and V2c corresponding to interatomic distances d1c and d2c, respectively. The effective Λ-type system of the target atoms is coupled to the control atom with RRI strength (V1c+V2c). In addition, the control atom is excited resonantly by another AM field from |0c to |rc with Rabi frequency Ωc(t).
Fig. 2.
Fig. 2. Time-dependent average fidelities of the SWAP gate with {δ=0, T=3.87μs} and {δ/2π=1.11MHz, T=33.28μs}, respectively. Atomic decay is not considered.
Fig. 3.
Fig. 3. Rydberg excitation probabilities during the SWAP gate procedure with different excitation numbers for (a) the resonant RAB with δ=0 and (b) the modified RAB with δ/2π=1.11MHz, respectively. Two-atom initial product state |Ψ0=(|01+|11)/2|12 is specified.
Fig. 4.
Fig. 4. Infidelities of the SWAP gates caused by (a) atomic decay with different lifetimes of the Rydberg state, (b) motional dephasing with different atomic temperatures, (c) standard deviations of the interatomic distance, and (d) deviations in the RRI strength. Each point in (b), (c), and (d) denotes the average of 201 results.
Fig. 5.
Fig. 5. Time-dependent average fidelities of the CSWAP gate with {δ=0, T=3.87μs} and {δ/2π=1.11MHz, T=33.28μs}, respectively. Atomic decay is not considered. Ωcm/2π=12MHz and ωc/2π=142MHz, and V1c/2π=V2c/2π=70.98MHz.
Fig. 6.
Fig. 6. Rydberg excitation probabilities during the CSWAP gate procedure with different excitation numbers for (a) the resonant RAB with δ=0 and (b) the modified RAB with δ/2π=1.11MHz, respectively. Three-atom initial product state |Ψ0=(01|11)/2(|02|12)/2(|0c|1c)/2 is specified.
Fig. 7.
Fig. 7. Infidelities of the CSWAP gates caused by (a) atomic decay with different lifetimes of the Rydberg state, (b) motional dephasing with different atomic temperatures, (c) standard deviations of the distance between the two target atoms, and (d) deviations in the RRI strength between the two target atoms. Each point in (b), (c), and (d) denotes the average of 201 results.

Equations (20)

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H^12=H^1I^2+I^1H^2+V|rrrr|,
H^j=k=01Ωk(t)2|kjr|+H.c.
H^e=[Ωe2(|01rr|+|10rr|)+H.c.]+δ|rrrr|,
ρ˙=i[ρ,H^Full]12j=1Nk=02(L^kjL^kjρ2L^kjρL^kj+ρL^kjL^kj),
H^dd=Ωdd2(|01+|10)(01|+10|),
H^12c=H^12I^c+I^1I^2H^c+I^1V2c|rr2crr|+V1c|r1r|I^2|rcr|,
H^12c=H^eI^c+I^1I^2H^c+(V1c+V2c)|rrrrrr|,
H^eff=H^e|1c1|,
H^0=12[Ω0mcos(ω0t)(|00r0|+|01r1|+|0rrr|+|000r|+|101r|+|r0rr|)+Ω1mcos(ω1t)(|10r0|+|11r1|+|1rrr|+|010r|+|111r|+|r1rr|)+H.c.]+V|rrrr|.
H^1=Ω0m4{(eiω0t+eiω0t)(|00r0|+|01r1|+|000r|+|101r|)+[ei(ω0δ)t+eiω1t](|0rrr|+|r0rr|)}+Ω1m4{(eiω1t+eiω1t)(|10r0|+|11r1|+|010r|+|111r|)+[eiω0t+ei(ω1+δ)t](|1rrr|+|r1rr|)}+H.c.
Ω0m4(eiω0t+eiω0t)(|00r0|+|000r|)+Ω1m4(eiω1t+eiω1t)(|11r1|+|111r|)+H.c.
H^1[Ω0m4(eiω0t+eiω0t)|01r1|+Ω1m4eiω0t|r1rr|]+[Ω1m4(eiω1t+eiω1t)|010r|+Ω0m4eiω1t|0rrr|]+[Ω0m4(eiω0t+eiω0t)|101r|+Ω1m4eiω0t|1rrr|]+[Ω1m4(eiω1t+eiω1t)|10r0|+Ω0m4eiω0t|r0rr|]+Ω0m4ei(ω0δ)t(|0rrr|+|r0rr|)+Ω1m4ei(ω1+δ)t(|1rrr|+|r1rr|)+H.c.
H^e=[Ωe2(|01rr|+|10rr|)+H.c.]+δ|rrrr|,
F¯(ε,U^)={j=14Ntr[U^u^jU^ε(u^j)]+l2}/l2(l+1),
H^2=Ωcm4(eiωct+eiωct)(|01012c01r|+|10012c10r|+|rr012crrr|)+Ωe2(|01012crr0|+|10012crr0|+|01r12crrr|+|10r12crrr|)+H.c.
H^3=Ωcm4[(eiωct+eiωct)(|01012c01r|+|10012c10r|)+(1+e2iωct)|rr012crrr|]+Ωe2(|01012crr0|+|10012crr0|+|01r12crrr|eiωct+|10r12crrr|eiωct)+H.c.
H^3=[Ωcm4|rr012crrr|+Ωe2(|01012crr0|+|10012crr0|)+H.c.]+Δrrr|rrr12crrr|,
H^4=[Ωe2(|01012c+|10012c)(ϕ0|+ϕ1|)+H.c.]+Ωcm4n=01(1)n|ϕnϕn|+δ|rr12rr|,
H^5=Ωe2(|01012c+|10012c)[ϕ0|eit(Ωcm/4+δ)+ϕ1|eit(Ωcm/4δ)]+H.c.
H^eff=[Ωe2(|01112c+|10112c)rr1|+H.c.]+δ|rr112crr1|,