Abstract

Encoding qubits in multiple degrees of freedom (DOFs) of a quantum system allows less-decoherence quantum information processing with much less quantum resources. We present a compact and scalable quantum circuit to determinately implement a hyper-parallel controlled-controlled-phase-flip (hyper-C2PF) gate in a three-photon system in both the polarization and spatial DOFs. In contrast with the one with many qubits encoding on one DOF only, our hyper-C2PF gate operating two independent C2PF gates on a three-photon system with less decoherence, and reduces the quantum resources required in quantum information processing by a half. Additional photons, necessary for many approaches, are not required in the present scheme. Our calculation shows that this hyper-C2PF gate is feasible in experiment.

© 2016 Optical Society of America

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Scalable photonic quantum computing assisted by quantum-dot spin in double-sided optical microcavity

Hai-Rui Wei and Fu-Guo Deng
Opt. Express 21(15) 17671-17685 (2013)

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2016 (1)

S. Sun, H. Kim, G. S. Solomon, and E. Waks, “A quantum phase switch between a single solid-state spin and a photon,” Nat. Nanotech. 11, 539 (2016).
[Crossref]

2015 (9)

L. Zhou and Y. B. Sheng, “Complete logic Bell-state analysis assisted with photonic Faraday rotation,” Phys. Rev. A 92, 042314 (2015).
[Crossref]

D. G. England, K. A. G. Fisher, J. P. W. MacLean, P. J. Bustard, R. Lausten, K. J. Resch, and B. J. Sussman, “Storage and retrieval of THz-bandwidth single photons using a room-temperature diamond quantum memory,” Phys. Rev. Lett. 114, 053602 (2015).
[Crossref] [PubMed]

H. Kosaka and N. Niikura, “Entangled absorption of a single photon with a single spin in diamond,” Phys. Rev. Lett. 114, 053603 (2015).
[Crossref] [PubMed]

A. C. Santosand and M. S. Sarandy, “Superadiabatic controlled evolutions and universal quantum computation,” Sci. Rep. 5, 15775 (2015).
[Crossref]

M. Hua, M. J. Tao, and F. G. Deng, “Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED,” Sci. Rep. 5, 9274 (2015).
[Crossref] [PubMed]

M. Hua, M. J. Tao, F. G. Deng, and G. L. Long, “One-step resonant controlled-phase gate on distant transmon qutrits in different 1D superconducting resonators,” Sci. Rep. 5, 14541 (2015).
[Crossref] [PubMed]

B. C. Ren, G. Y. Wang, and F. G. Deng, “Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime,” Phys. Rev. A 91, 032328 (2015).
[Crossref]

Y. B. Sheng and L. Zhou, “Deterministic entanglement distillation for secure double-server blind quantum computation,” Sci. Rep. 5, 7815 (2015).
[Crossref] [PubMed]

H. R. Wei and G. L. Long, “Universal photonic quantum gates assisted by ancilla diamond nitrogen-vacancy centers coupled to resonators,” Phys. Rev. A 91, 032324 (2015).
[Crossref]

2014 (12)

T. J. Wang and C. Wang, “Universal hybrid three-qubit quantum gates assisted by a nitrogen-vacancy center coupled with a whispering-gallery-mode microresonator,” Phys. Rev. A 90, 052310 (2014).
[Crossref]

T. J. Wang, Y. Zhang, and C. Wang, “Universal hybrid hyper-controlled quantum gates assisted by quantum dots in optical double-sided microcavities,” Laser Phys. Lett. 11, 025203 (2014).
[Crossref]

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,” Sci. Rep. 4, 4623 (2014).
[Crossref] [PubMed]

H. R. Wei and F. G. Deng, “Scalable quantum computing based on stationary spin qubits in coupled quantum dots inside double-sided optical microcavities,” Sci. Rep. 4, 7551 (2014).
[Crossref] [PubMed]

M. Zwerger, H. J. Briegel, and W. Dür, “Hybrid architecture for encoded measurement-based quantum computation,” Sci. Rep. 4, 5364 (2014).
[Crossref] [PubMed]

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240 (2014).
[Crossref]

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletic, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature (London) 508, 241–244 (2014).
[Crossref]

Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent optical transitions in implanted nitrogen vacancy centers,” Nano Lett. 14, 1982–1986 (2014).
[Crossref] [PubMed]

S. Arroyo-Camejo, A. Lazariev, S. W. Hell, and G. Balasubramanian, “Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin,” Nat. Commun. 5, 4870 (2014).
[Crossref] [PubMed]

C. Zu, W. B. Wang, L. He, W. G. Zhang, C. Y. Dai, F. Wang, and L. M. Duan, “Experimental realization of universal geometric quantum gates with solid-state spins,” Nature (London) 514, 72–75 (2014).
[Crossref]

L. Zhou and Y. B. Sheng, “Detection of nonlocal atomic entanglement assisted by single photons,” Phys. Rev. A 90, 024301 (2014).
[Crossref]

H. R. Wei and F. G. Deng, “Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities,” Opt. Express 22, 593–607 (2014).
[Crossref] [PubMed]

2013 (12)

H. R. Wei and F. G. Deng, “Scalable photonic quantum computing assisted by quantum-dot spin in double-sided optical microcavity,” Opt. Express 21, 17671–17685 (2013).
[Crossref] [PubMed]

C. Wang, Y. Zhang, R. Z. Jiao, and G. S. Jin, “Universal quantum controlled phase gates on photonic qubits based on nitrogen vacancy centers and microcavity resonators,” Opt. Express 21, 19252–19260 (2013).
[Crossref] [PubMed]

R. Albrecht, A. Bommer, C. Deutsch, J. Reichel, and C. Becher, “Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity,” Phys. Rev. Lett. 110, 243602 (2013).
[Crossref] [PubMed]

N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budke, and R. L. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743 (2013).
[Crossref] [PubMed]

P. Siyushev, H. Pinto, M. Vörös, A. Gali, F. Jelezko, and J. Wrachtrup, “Optically controlled switching of the charge state of a single nitrogen-vacancy center in diamond at cryogenic temperatures,” Phys. Rev. Lett. 110, 167402 (2013).
[Crossref] [PubMed]

H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, “Heralded entanglement between solid-state qubits separated by three metres,” Nature (London) 497, 86–90 (2013).
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G. Feng, G. Xu, and G. Long, “Experimental realization of nonadiabatic holonomic quantum computation,” Phys. Rev. Lett. 110, 190501 (2013).
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N. Yu, R. Duan, and M. Ying, “Five two-qubit gates are necessary for implementing the Toffoli gate,” Phys. Rev. A 88, 010304(R) (2013).
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B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity,” Laser Phys. Lett. 10, 095202 (2013).
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H. R. Wei and F. G. Deng, “Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities,” Phys. Rev. A 88, 042323 (2013).
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D. Solenov, S. E. Economou, and T. L. Reinecke, “Fast two-qubit gates for quantum computing in semiconductor quantum dots using a photonic microcavity,” Phys. Rev. B 87, 035308 (2013).
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B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser Phys. Lett. 10, 115201 (2013).
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2012 (6)

D. Pile, “How many bits can a photon carry ?” Nature Photon. 6, 14–15 (2012).
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A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, “Implementation of a Toffoli gate with superconducting circuits,” Nature (London) 481, 170 (2012).
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V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K. M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical Resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
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J. Hagemeier, C. Bonato, T. A. Truong, H. Kim, G. J. Beirne, M. Bakker, M. P. van Exter, Y. Luo, P. Petroff, and D. Bouwmeester, “H1 photonic crystal cavities for hybrid quantum information protocols,” Opt. Express 20, 24714–24726 (2012).
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T. van der Sar, Z. H. Wang, M. S. Blok, H. Bernien, T. H. Taminiau, D. M. Toyli, D. A. Lidar, D. D. Awschalom, R. Hanson, and V. V. Dobrovitski, “Decoherence-protected quantum gates for a hybrid solid-state spin register,” Nature (London) 484, 82–86 (2012).
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B. J. M. Hausmann, B. Shields, Q. Quan, P. Maletinsky, M. McCutcheon, J. T. Choy, T. M. Babinec, A. Kubanek, A. Yacoby, M. D. Lukin, and M. Loncar, “Integrated diamond networks for quantum nanophotonics,” Nano Lett. 12, 1578–1582 (2012).
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2011 (6)

P. E. Barclay, K. M. C. Fu, C. Santori, A. Faraon, and R. G. Beausoleil, “Hybrid nanocavity resonant enhancement of color center emission in diamond,” Phys. Rev. X 1, 011007 (2011).

J. R. Maze, A. Gali, E. Togan, Y. Chu, A. Trifonov, E. Kaxiras, and M. D. Lukin, “Properties of nitrogen-vacancy centers in diamond: The group theoretic approach,” New J. Phys. 13, 025025 (2011).
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L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, and R. Hanson, “High-fidelity projective read-out of a solid-state spin quantum register,” Nature (London) 477, 574–578 (2011).
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C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,” Phys. Rev. B 84, 075306 (2011).
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L. C. Bassett, F. J. Heremans, C. G. Yale, B. B. Buckley, and D. D. Awschalom, “Electrical tuning of single nitrogen-vacancy center optical transitions enhanced by photoinduced fields,” Phys. Rev. Lett. 107, 266403 (2011).
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A. Majumdar, E. D. Kim, and J. Vučković, “Effect of photogenerated carriers on the spectral diffusion of a quantum dot coupled to a photonic crystal cavity,” Phys. Rev. B 84, 195304 (2011).
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2010 (6)

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
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E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London) 466, 730–734 (2010).
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P. Zhang, R. F. Liu, Y. F. Huang, H. Gao, and F. L. Li, “Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer,” Phys. Rev. A 82, 064302 (2010).
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Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
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G. Vallone, G. Donati, N. Bruno, A. Chiuri, and P. Mataloni, “Experimental realization of the Deutsch-Jozsa algorithm with a six-qubit cluster state,” Phys. Rev. A 81, 050302(R) (2010).
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G. Vallone, G. Donati, R. Ceccarelli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation,” Phys. Rev. A 81, 052301 (2010).
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2009 (10)

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
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C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B 80, 205326 (2009).
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L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature (London) 460, 240 (2009).
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T. Monz, K. Kim, W. Hänsel, M. Riebe, A. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, “Realization of the quantum Toffoli gate with trapped ions,” Phys. Rev. Lett. 102, 040501 (2009).
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R. Ceccarelli, G. Vallone, F. D. Martini, P. Mataloni, and A. Cabello, “Experimental entanglement and nonlocality of a two-photon six-qubit cluster state,” Phys. Rev. Lett. 103, 160401 (2009).
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G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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A. Batalov, V. Jacques, F. Kaiser, P. Siyushev, P. Neumann, L. J. Rogers, R. L. McMurtrie, N. B. Manson, F. Jelezko, and J. Wrachtrup, “Low temperature studies of the excited-state structure of negatively charged nitrogen-vacancy color centers in diamond,” Phys. Rev. Lett. 102, 195506 (2009).
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J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79, 032303 (2009).
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G. D. Fuchs, V. V. Dobrovitski, D. M. Toyli, F. J. Heremans, and D. D. Awschalom, “Gigahertz dynamics of a strongly driven single quantum spin,” Science 326, 1520–1522 (2009).
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K. M. C. Fu, C. Santori, P. E. Barclay, L. J. Rogers, N. B. Manson, and R. G. Beausoleil, “Observation of the dynamic Jahn-Teller effect in the excited states of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 103, 256404 (2009).
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2008 (3)

C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B 78, 085307 (2008).
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Y. Liu, G. L. Long, and Y. Sun, “Analytic one-bit and CNOT gate constructions of general n-qubit controlled gates,” Int. J. Quantum Inf. 6, 447–462 (2008).
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2007 (1)

M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science 316, 1312–1316 (2007).
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2006 (4)

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006).
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M. Scholz, T. Aichele, S. Ramelow, and O. Benson, “Deutsch-Jozsa algorithm using triggered single photons from a single quantum dot,” Phys. Rev. Lett. 96, 180501 (2006).
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N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
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2004 (3)

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
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L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
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Y. Y. Shi, “Both Toffoli and controlled-NOT need little help to universal quantum computing,” Quant. Inf. Comput. 3, 084–092 (2003).

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001).
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1996 (1)

J. A. Smolin and D. P. DiVincenzo, “Five two-bit quantum gates are sufficient to implement the quantum Fredkin gate,” Phys. Rev. A 53, 2855 (1996).
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1995 (1)

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457 (1995).
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G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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Acosta, V. M.

V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K. M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical Resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
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Aichele, T.

M. Scholz, T. Aichele, S. Ramelow, and O. Benson, “Deutsch-Jozsa algorithm using triggered single photons from a single quantum dot,” Phys. Rev. Lett. 96, 180501 (2006).
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Albrecht, R.

R. Albrecht, A. Bommer, C. Deutsch, J. Reichel, and C. Becher, “Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity,” Phys. Rev. Lett. 110, 243602 (2013).
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Alkemade, P. F. A.

L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, and R. Hanson, “High-fidelity projective read-out of a solid-state spin quantum register,” Nature (London) 477, 574–578 (2011).
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Almeida, M. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
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An, J. H.

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A 79, 032303 (2009).
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Arroyo-Camejo, S.

S. Arroyo-Camejo, A. Lazariev, S. W. Hell, and G. Balasubramanian, “Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin,” Nat. Commun. 5, 4870 (2014).
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Awschalom, D. D.

T. van der Sar, Z. H. Wang, M. S. Blok, H. Bernien, T. H. Taminiau, D. M. Toyli, D. A. Lidar, D. D. Awschalom, R. Hanson, and V. V. Dobrovitski, “Decoherence-protected quantum gates for a hybrid solid-state spin register,” Nature (London) 484, 82–86 (2012).
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L. C. Bassett, F. J. Heremans, C. G. Yale, B. B. Buckley, and D. D. Awschalom, “Electrical tuning of single nitrogen-vacancy center optical transitions enhanced by photoinduced fields,” Phys. Rev. Lett. 107, 266403 (2011).
[Crossref]

G. D. Fuchs, V. V. Dobrovitski, D. M. Toyli, F. J. Heremans, and D. D. Awschalom, “Gigahertz dynamics of a strongly driven single quantum spin,” Science 326, 1520–1522 (2009).
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Babinec, T. M.

B. J. M. Hausmann, B. Shields, Q. Quan, P. Maletinsky, M. McCutcheon, J. T. Choy, T. M. Babinec, A. Kubanek, A. Yacoby, M. D. Lukin, and M. Loncar, “Integrated diamond networks for quantum nanophotonics,” Nano Lett. 12, 1578–1582 (2012).
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Bakker, M.

Balasubramanian, G.

S. Arroyo-Camejo, A. Lazariev, S. W. Hell, and G. Balasubramanian, “Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin,” Nat. Commun. 5, 4870 (2014).
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G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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Barbieri, M.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
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Barclay, P. E.

P. E. Barclay, K. M. C. Fu, C. Santori, A. Faraon, and R. G. Beausoleil, “Hybrid nanocavity resonant enhancement of color center emission in diamond,” Phys. Rev. X 1, 011007 (2011).

K. M. C. Fu, C. Santori, P. E. Barclay, L. J. Rogers, N. B. Manson, and R. G. Beausoleil, “Observation of the dynamic Jahn-Teller effect in the excited states of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 103, 256404 (2009).
[Crossref]

Barenco, A.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457 (1995).
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N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budke, and R. L. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743 (2013).
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Bassett, L. C.

L. C. Bassett, F. J. Heremans, C. G. Yale, B. B. Buckley, and D. D. Awschalom, “Electrical tuning of single nitrogen-vacancy center optical transitions enhanced by photoinduced fields,” Phys. Rev. Lett. 107, 266403 (2011).
[Crossref]

Batalov, A.

A. Batalov, V. Jacques, F. Kaiser, P. Siyushev, P. Neumann, L. J. Rogers, R. L. McMurtrie, N. B. Manson, F. Jelezko, and J. Wrachtrup, “Low temperature studies of the excited-state structure of negatively charged nitrogen-vacancy color centers in diamond,” Phys. Rev. Lett. 102, 195506 (2009).
[Crossref] [PubMed]

Baur, M.

A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, “Implementation of a Toffoli gate with superconducting circuits,” Nature (London) 481, 170 (2012).
[Crossref]

Beausoleil, R. G.

V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K. M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical Resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
[Crossref] [PubMed]

P. E. Barclay, K. M. C. Fu, C. Santori, A. Faraon, and R. G. Beausoleil, “Hybrid nanocavity resonant enhancement of color center emission in diamond,” Phys. Rev. X 1, 011007 (2011).

K. M. C. Fu, C. Santori, P. E. Barclay, L. J. Rogers, N. B. Manson, and R. G. Beausoleil, “Observation of the dynamic Jahn-Teller effect in the excited states of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 103, 256404 (2009).
[Crossref]

Becher, C.

R. Albrecht, A. Bommer, C. Deutsch, J. Reichel, and C. Becher, “Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity,” Phys. Rev. Lett. 110, 243602 (2013).
[Crossref] [PubMed]

Beck, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
[Crossref] [PubMed]

Beirne, G. J.

Bennett, C. H.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457 (1995).
[Crossref] [PubMed]

Benson, O.

M. Scholz, T. Aichele, S. Ramelow, and O. Benson, “Deutsch-Jozsa algorithm using triggered single photons from a single quantum dot,” Phys. Rev. Lett. 96, 180501 (2006).
[Crossref] [PubMed]

Bernien, H.

H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, “Heralded entanglement between solid-state qubits separated by three metres,” Nature (London) 497, 86–90 (2013).
[Crossref]

T. van der Sar, Z. H. Wang, M. S. Blok, H. Bernien, T. H. Taminiau, D. M. Toyli, D. A. Lidar, D. D. Awschalom, R. Hanson, and V. V. Dobrovitski, “Decoherence-protected quantum gates for a hybrid solid-state spin register,” Nature (London) 484, 82–86 (2012).
[Crossref]

L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, and R. Hanson, “High-fidelity projective read-out of a solid-state spin quantum register,” Nature (London) 477, 574–578 (2011).
[Crossref]

Bishop, L. S.

L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature (London) 460, 240 (2009).
[Crossref]

Blais, A.

L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature (London) 460, 240 (2009).
[Crossref]

Blatt, R.

T. Monz, K. Kim, W. Hänsel, M. Riebe, A. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, “Realization of the quantum Toffoli gate with trapped ions,” Phys. Rev. Lett. 102, 040501 (2009).
[Crossref] [PubMed]

Blok, M. S.

H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, “Heralded entanglement between solid-state qubits separated by three metres,” Nature (London) 497, 86–90 (2013).
[Crossref]

T. van der Sar, Z. H. Wang, M. S. Blok, H. Bernien, T. H. Taminiau, D. M. Toyli, D. A. Lidar, D. D. Awschalom, R. Hanson, and V. V. Dobrovitski, “Decoherence-protected quantum gates for a hybrid solid-state spin register,” Nature (London) 484, 82–86 (2012).
[Crossref]

Bommer, A.

R. Albrecht, A. Bommer, C. Deutsch, J. Reichel, and C. Becher, “Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity,” Phys. Rev. Lett. 110, 243602 (2013).
[Crossref] [PubMed]

Bonato, C.

J. Hagemeier, C. Bonato, T. A. Truong, H. Kim, G. J. Beirne, M. Bakker, M. P. van Exter, Y. Luo, P. Petroff, and D. Bouwmeester, “H1 photonic crystal cavities for hybrid quantum information protocols,” Opt. Express 20, 24714–24726 (2012).
[Crossref] [PubMed]

C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,” Phys. Rev. B 84, 075306 (2011).
[Crossref]

Bouwmeester, D.

J. Hagemeier, C. Bonato, T. A. Truong, H. Kim, G. J. Beirne, M. Bakker, M. P. van Exter, Y. Luo, P. Petroff, and D. Bouwmeester, “H1 photonic crystal cavities for hybrid quantum information protocols,” Opt. Express 20, 24714–24726 (2012).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1 A ∧-type atom-like structure of the negatively-charged NV centre confined in an optical resonator. The states |±〉 act as the computational basis states, and the state |0〉 acts as an ancilla employed for spin manipulation. The optical transitions from the ground states |±〉 to the ancillary state |A2〉 are coupled by the σ circularly polarized photons, respectively.
Fig. 2
Fig. 2 Compact quantum circuit for implementing hyper-parallel C2PF gate on a three-photon system with both the spatial and polarization DOFs. CPBS i (i = 1, 2, · · ·, 34) represents a circular polarizing beam splitter that transmits the right circular polarizations (R) and reflects the left circular polarizations (L). Hi (i = 1, 2, · · ·, 8) represents a Hadamard operation performed on the passing photon with a half-wave plate oriented at 22.5°. Xj (j = 1, 2, · · ·, 10) represents a bit-flip operation performed on the passing photon with a half-wave plate oriented at 45°. BS k (k = 1, 2, 3, 4) is a balanced polarization-preserving beam splitter.
Fig. 3
Fig. 3 The average fidelities (, red solid curve) and efficiencies (η̄, blue dashed curve) of the hyper-C2PF gate as a function of g / κ γ . g / κ γ 0.5 .

Tables (1)

Tables Icon

Table 1 The classical feed-forward operations on the photonic qubits to complete a full and deterministic hyper-C2PF gate conditioned on the outcomes of the NV centre spins. σz = |R〉 〈R| − |L〉 〈L|. Phase shifter π performed on the spatial mode a1 (b2) completes the transformation |a1〉 → −|a1〉 (|b2〉 → −|b2〉).

Equations (22)

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d a ^ d t = [ i ( ω c ω p ) + κ 2 ] a ^ ( t ) g σ ( t ) κ a ^ in , d σ d t = [ i ( ω 0 ω p ) + γ 2 ] σ ( t ) g σ z ( t ) a ^ ( t ) + γ σ z ( t ) b ^ in ( t ) ,
r ( ω p ) = a ^ out a ^ in = [ i ( ω c ω p ) κ 2 ] [ i ( ω 0 ω p ) + γ 2 ] + g 2 [ i ( ω c ω p ) + κ 2 ] [ i ( ω 0 ω p ) + γ 2 ] + g 2 .
| R | + r ( ω p ) | R | + = e i φ | r ( ω p ) | | R | + , | L | + r 0 ( ω p ) | L | + = e i φ 0 | r 0 ( ω p ) | | L | + .
| R | r 0 ( ω p ) | R | = e i φ 0 | r 0 ( ω p ) | | R | , | L | r ( ω p ) | L | = e i φ | r ( ω p ) | | L | .
r = κ γ + 4 g 2 κ γ + 4 g 2 , r 0 = 1 .
| R | + | R | + , | R | | R | , | L | + | L | + , | L | | L | .
| φ a = ( α 1 | R 1 + α 2 | L 1 ) ( ς 1 | a 1 + ς 2 | a 2 ) , | φ b = ( β 1 | R 2 + β 2 | L 2 ) ( ζ 1 | b 1 + ζ 2 | b 2 ) , | φ c = ( δ 1 | R 3 + δ 2 | L 3 ) ( ξ 1 | c 1 + ξ 2 | c 2 ) .
| φ e 1 , 3 = | + 1 , 3 + | 1 , 3 2 , | φ e 2 , 4 = | + 2 , 4 | 2 , 4 2 .
| + 1 2 ( | + + | ) , | 1 2 ( | + | ) .
| φ 0 = | φ a | φ b | φ c | φ e 1 | φ e 2 | φ e 3 | φ e 4 ,
| φ 1 = | φ a | φ c | φ e 2 | φ e 3 | φ e 4 ( ζ 1 | b 1 + ζ 2 | b 2 ) ( β 1 | R 2 | 1 + β 2 | L 2 | + 1 ) .
φ 2 = | φ a | φ e 2 | φ e 3 | φ e 4 ( ζ 1 | b 1 + ζ 2 | b 2 ) ( δ 1 | R 3 + δ 2 | L 3 ) [ β 1 | R 2 ( ξ 1 | c 1 ξ 2 | c 3 ) | 1 + β 2 | L 2 ( ξ 1 | c 1 + ξ 2 | c 2 ) | + 1 ] .
| c 2 1 2 ( | c 2 + | c 3 ) , | c 3 1 2 ( | c 2 | c 3 ) .
| φ 3 = ( ς 1 | a 1 + ς 2 | a 2 ) | ζ 1 | b 1 + ζ 2 | b 2 ( δ 1 | R 3 + δ 2 | L 3 ) ( α 1 | R 1 | + 2 + α 2 | L 1 | 2 ) [ β 1 | R 2 ( ξ 1 | c 1 ξ 2 | c 3 ) | 1 + β 2 | L 2 ( ξ 1 | c 1 + ξ 2 | c 2 ) | + 1 ] | φ e 3 | φ e 4 .
| φ 4 = ( ς 1 | a 1 + ς 2 | a 2 ) ( ζ 1 | b 1 + ζ 2 | b 2 ) ( δ 1 | R 3 + δ 2 | L 3 ) { α 1 | R 1 | + 2 ( β 1 | R 2 | 1 + β 2 | L 2 | + 1 ) ( ξ 1 | c 1 + ξ 2 | c 2 ) + α 2 | L 1 | 2 [ β 1 | R 2 | 1 ( ξ 1 | c 1 + ξ 2 | c 2 ) + β 2 | L 2 | + 1 ( ξ 1 | c 1 ξ 2 | c 2 ) ] } | φ e 3 | φ e 4 .
| φ 5 = { α 1 | R 1 | + 2 ( β 1 | R 2 | 1 + β 2 | L 2 | + 1 ) ( ξ 1 | c 1 + ξ 2 | c 2 ) + α 2 | L 1 | 2 [ β 1 | R 2 | 1 ( ξ 1 | c 1 + ξ 2 | c 2 ) + β 2 | L 2 | + 1 ( ξ 1 | c 1 ξ 2 | c 2 ) ] } ( ς 1 | a 1 + ς 2 | a 2 ) ( ζ 1 | b 1 | + 3 + ζ 2 | b 2 | 3 ) ( δ 1 | R 3 + δ 2 | L 3 ) | φ e 4 .
| φ 6 = { α 1 | R 1 | + 2 ( β 1 | R 2 | 1 + β 2 | L 2 | + 1 ) ( ξ 1 | c 1 + ξ 2 | c 2 ) + α 2 | L 1 | 2 [ β 1 | R 2 | 1 ( ξ 1 | c 1 + ξ 2 | c 2 ) + β 2 | L 2 | + 1 ( ξ 1 | c 1 ξ 2 | c 2 ) ] } ( ς 1 | a 1 + ς 2 | a 2 ) [ ζ 1 | b 1 ( δ 1 | R 3 + δ 2 | R 3 ) | + 3 + ζ 2 | b 2 ( δ 1 | R 3 + δ 2 | L 3 ) | 3 ] | φ e 4 .
| φ 7 = { α 1 | R 1 | + 2 ( β 1 | R 2 | 1 + β 2 | L 2 | + 1 ) ( ξ 1 | c 1 + ξ 2 | c 2 ) + α 2 | L 1 | 2 [ β 1 | R 2 | 1 ( ξ 1 | c 1 + ξ 2 | c 2 ) + β 2 | L 2 | + 1 ( ξ 1 | c 1 ξ 2 | c 2 ) ] } ( ς 1 | a 1 | 4 + ς 2 | a 2 | + 4 ) [ ζ 1 | b 1 ( δ 1 | R 3 + δ 2 | R 3 ) | + 3 + ζ 2 | b 2 ( δ 1 | R 3 + δ 2 | L 3 ) | 3 ] .
| φ 8 = { α 1 | R 1 | + 2 [ ( β 1 | R 2 | 1 + β 2 | L 2 | + 1 ) ( ξ 1 | c 1 + ξ 2 | c 2 ) ] + α 2 | L 1 | 2 [ β 1 | R 2 ( ξ 1 | c 1 + ξ 2 | c 2 ) | 1 + β 2 | L 2 ( ξ 1 | c 1 ξ 2 | c 2 ) | + 1 ] } { ς 1 | a 1 | 4 [ ( ζ 1 | b 1 | + 3 + ζ 2 | b 2 | 3 ) ( δ 1 | R 3 + δ 2 | L 3 ) ] + ς 2 | a 2 | + 4 [ ζ 1 | b 1 ( δ 1 | R 3 + δ 2 | L 3 ) | + 3 + ζ 2 | b 2 ( δ 1 | R 3 δ 2 | L 3 ) | 3 ] } .
| φ 9 = { ( α 1 β 1 | R 1 | R 2 + α 1 β 2 | R 1 | L 2 + α 2 β 1 | L 1 | R 2 ) ( ξ 1 | c 1 + ξ 2 | c 2 ) + α 2 β 2 | L 1 | L 2 ( ξ 1 | c 1 ξ 2 | c 2 ) } { ( ς 1 ζ 1 | a 1 | b 1 + ς 1 ζ 2 | a 1 | b 2 + ς 2 ζ 1 | a 2 | b 1 ) ( δ 1 | R 3 + δ 2 | L 3 ) + ς 2 ζ 2 | a 2 | b 2 ( δ 1 | R 3 δ 2 | L 3 ) } .
F ¯ = 1 ( 2 π ) 6 0 2 π d α 0 2 π d β 0 2 π d γ 0 2 π d ς 0 2 π d ζ 0 2 π d ξ | ψ out | ψ out | 2 .
η ¯ = 1 ( 2 π ) 6 0 2 π d α 0 2 π d β 0 2 π d γ 0 2 π d ς 0 2 π d ζ 0 2 π d ξ n output n input = [ 121 + ( 128 | r | + 164 | r | 2 + 40 | r | 3 + 14 | r | 4 + | r | 5 ( 2 + | r | ) 2 ( 4 + | r | ) ) × ( 91 + 58 | r | + 42 | r | 2 + 18 | r | 3 + 12 | r | 4 + 14 | r | 5 + 14 | r | 6 + | r | 7 ( 6 + | r | ) ] / 131072 .

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