Abstract

Under the balance condition of the diamond nitrogen vacancy center embedded in an optical cavity as a result of cavity quantum electrodynamics, we present a robust hyperparallel photonic controlled-phase-flip gate for a two-photon system in both the polarization and spatial-mode degrees of freedom (DOFs), in which the noise caused by the inequality of two reflection coefficients can be depressed efficiently. This gate doubles the quantum entangling operation synchronously on a photon system and can reduce the quantum resources consumed largely and depress the photonic dissipation efficiently, compared with the two cascade quantum entangling gates in one DOF. It has a near unit fidelity. Moreover, we show that the balance condition can be obtained in both the weak coupling regime and the strong coupling regime, and the high-fidelity quantum gate operation is easier to be realized in the balance condition than the ones in the ideal condition in experiment.

© 2017 Optical Society of America

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Simple schemes for universal quantum gates with nitrogen-vacancy centers in diamond

Liu-Yong Cheng, Hong-Fu Wang, and Shou Zhang
J. Opt. Soc. Am. B 30(7) 1821-1826 (2013)

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2016 (7)

Z. Y. Xue, Z. Q. Yin, Y. Chen, Z. D. Wang, and S. L. Zhu, “Topological quantum memory interfacing atomic and superconducting qubits,” Sci. China Phys. Mech. Astron. 59, 660301 (2016).
[Crossref]

Y. B. Sheng, J. Pan, R. Guo, L. Zhou, and L. Wang, “Efficient N-particle W state concentration with different parity check gates,” Sci. China Phys. Mech. Astron. 59, 660301 (2016).

L. Y. He, T. J. Wang, and C. Wang, “Construction of high-dimensional universal quantum logic gates using a Λ system coupled with a whispering-gallery-mode microresonator,” Opt. Express 24, 15429–15445 (2016).
[Crossref] [PubMed]

M. Gao, F. C. Lei, C. G. Du, and G. L. Long, “Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regimes,” Sci. China Phys. Mech. Astron. 59, 610301 (2016).
[Crossref]

C. Y. Hu, “Spin-based single-photon transistor, dynamic random access memory, diodes, and routers in semiconductors,” Phys. Rev. B 94, 245307 (2016).
[Crossref]

T. Li and G. L. Long, “Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities,” Phys. Rev. A 94, 022343 (2016).
[Crossref]

T. Li and Z. Q. Yin, “Quantum superposition, entanglement, and state teleportation of a microorganism on an electromechanical oscillator,” Sci. Bull. 61, 163–171 (2016).
[Crossref]

2015 (10)

R. Heilmann, M. Gräfe, S. Nolte, and A. Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96–100 (2015).
[Crossref]

T. J. Wang, L. L. Liu, R. Zhang, C. Cao, and C. Wang, “One-step hyperentanglement purification and hyperdistillation with linear optics,” Opt. Express 23, 9284–9294 (2015).
[Crossref] [PubMed]

H. R. Wei and G. L. Long, “Hybrid quantum gates between flying photon and diamond nitrogen-vacancy centers assisted by optical microcavities,” Sci. Rep. 5, 12918 (2015).
[Crossref] [PubMed]

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518, 516–519 (2015).
[Crossref] [PubMed]

Q. Lin, “Optical parity gate and a wide range of entangled states generation,” Sci. China Phys. Mech. Astron. 58, 44201 (2015).
[Crossref]

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]

F. G. Deng, B. C. Ren, and X. H. Li, “Quantum hyperentanglement and its applications in quantum information processing,” Sci. Bull. 62, 46–68 (2015).
[Crossref]

Q. Liu and M. Zhang, “Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators,” Phys. Rev. A 91, 062321 (2015).
[Crossref]

X. H. Li and S. Ghose, “Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity,” Opt. Express 23, 3550–3562 (2015).
[Crossref] [PubMed]

X. H. Li and S. Ghose, “Hyperentanglement concentration for time-bin and polarization hyperentangled photons,” Phys. Rev. A 91, 062302 (2015).
[Crossref]

2014 (8)

B. C. Ren, F. F. Du, and F. G. Deng, “Two-step hyperentanglement purification with the quantum-state-joining method,” Phys. Rev. A 90, 052309 (2014).
[Crossref]

T. J. Wang, C. Cao, and C. Wang, “Linear-optical implementation of hyperdistillation from photon loss,” Phys. Rev. A 89, 052303 (2014).
[Crossref]

J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, “Strain coupling of a nitrogen-vacancy center spin to diamond mechanical oscillator,” Phys. Rev. Lett. 113, 020503 (2014).
[Crossref]

T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, “Nanophotonic quantum phase switch with a single atom,” Nature 508, 241–244 (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 508, 237–240 (2014).
[Crossref] [PubMed]

T. M. Graham and P. G. Kwiat, “Quantum hyperdense coding,” Proc. SPIE 9254, 92540B (2014).

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

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]

2013 (6)

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nat. Photonics 7, 521–526 (2013).
[Crossref]

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 497, 86–90 (2013).
[Crossref] [PubMed]

D. O’Shea, C. Junge, J. Volz, and A. Rauschenbeutel, “Fiber-optical switch controlled by a single atom,” Phys. Rev. Lett. 111, 193601 (2013).
[Crossref]

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics,” Phys. Rev. A 88, 012302 (2013).
[Crossref]

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]

G. Feng, G. Xu, and G. Long, “Experimental realization of nonadiabatic Holonomic quantum computation,” Phys. Rev. Lett. 110, 190501 (2013).
[Crossref] [PubMed]

2012 (6)

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 484, 82–86 (2012).
[Crossref] [PubMed]

B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, “Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities,” Opt. Express 20, 24664–24677 (2012).
[Crossref] [PubMed]

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities,” Phys. Rev. A 86, 042337 (2012).
[Crossref]

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
[Crossref] [PubMed]

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[Crossref] [PubMed]

A. Zheng, J. Li, R. Yu, X. Y. Lü, and Y. Wu, “Generation of Greenberger-Horne-Zeilinger state of distant diamond nitrogen-vacancy centers via nanocavity input-output process,” Opt. Express 20, 16902–16912 (2012).
[Crossref]

2011 (4)

Q. Chen, W. Yang, M. Feng, and J. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[Crossref]

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett. 106, 160501 (2011).
[Crossref] [PubMed]

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 477, 574–578 (2011).
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C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,” Phys. Rev. B 83, 115303 (2011).
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2010 (4)

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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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 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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B. B. Buckley, G. D. Fuchs, L. C. Bassett, and D. D. Awschalom, “Spin-light coherence for single-spin measurement and control in diamond,” Science 330, 1212–1215 (2010).
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2009 (7)

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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S. Schietinger, M. Barth, T. Aichele, and O. Benson, “Plasmon-enhanced single photon emission from a nanoassembled metal-diamond hybrid structure at room temperature,” Nano Lett. 9, 1694–1698 (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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L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. G. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
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P. E. Barclay, K. M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (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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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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2008 (4)

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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C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B 78, 125318 (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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J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
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2006 (2)

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (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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2005 (2)

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
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W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
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2004 (3)

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
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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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2003 (6)

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
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T. Yamamoto, Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425, 941–944 (2003).
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Y. Y. Shi, “Both Toffoli and controlled-not need little help to do universal quantum computation,” Quantum Inf. Comput. 3, 084 (2003).

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
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X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809 (2003).
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T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
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2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
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1997 (1)

N. A. Gershenfeld and I. L. Chuang, “Bulk spin-resonance quantum computation,” Science 275, 350–356 (1997).
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1996 (1)

A. Lenef and S. C. Rand, “Electronic structure of the N-V center in diamond: Theory,” Phys. Rev. B 53, 13441–13455 (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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Achard, 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).
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Acosta, V. M.

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
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Aichele, T.

S. Schietinger, M. Barth, T. Aichele, and O. Benson, “Plasmon-enhanced single photon emission from a nanoassembled metal-diamond hybrid structure at room temperature,” Nano Lett. 9, 1694–1698 (2009).
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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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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 477, 574–578 (2011).
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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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Aolita, L.

Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
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Aparo, L.

C. Vitelli, N. Spagnolo, L. Aparo, F. Sciarrino, E. Santamato, and L. Marrucci, “Joining the quantum state of two photons into one,” Nat. Photonics 7, 521–526 (2013).
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Appel, P.

J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, “Strain coupling of a nitrogen-vacancy center spin to diamond mechanical oscillator,” Phys. Rev. Lett. 113, 020503 (2014).
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Astafiev, O.

T. Yamamoto, Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425, 941–944 (2003).
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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 484, 82–86 (2012).
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B. B. Buckley, G. D. Fuchs, L. C. Bassett, and D. D. Awschalom, “Spin-light coherence for single-spin measurement and control in diamond,” Science 330, 1212–1215 (2010).
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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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Balasubramanian, G.

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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P. E. Barclay, K. M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (2009).
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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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J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, “Strain coupling of a nitrogen-vacancy center spin to diamond mechanical oscillator,” Phys. Rev. Lett. 113, 020503 (2014).
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Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
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Barth, M.

S. Schietinger, M. Barth, T. Aichele, and O. Benson, “Plasmon-enhanced single photon emission from a nanoassembled metal-diamond hybrid structure at room temperature,” Nano Lett. 9, 1694–1698 (2009).
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B. B. Buckley, G. D. Fuchs, L. C. Bassett, and D. D. Awschalom, “Spin-light coherence for single-spin measurement and control in diamond,” Science 330, 1212–1215 (2010).
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A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
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P. E. Barclay, K. M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (2009).
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F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
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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. 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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Benson, O.

S. Schietinger, M. Barth, T. Aichele, and O. Benson, “Plasmon-enhanced single photon emission from a nanoassembled metal-diamond hybrid structure at room temperature,” Nano Lett. 9, 1694–1698 (2009).
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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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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 497, 86–90 (2013).
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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 484, 82–86 (2012).
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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 477, 574–578 (2011).
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Blatt, R.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
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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 497, 86–90 (2013).
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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 484, 82–86 (2012).
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Branning, D.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
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Buckley, B. B.

B. B. Buckley, G. D. Fuchs, L. C. Bassett, and D. D. Awschalom, “Spin-light coherence for single-spin measurement and control in diamond,” Science 330, 1212–1215 (2010).
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Cai, X. D.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518, 516–519 (2015).
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T. J. Wang, L. L. Liu, R. Zhang, C. Cao, and C. Wang, “One-step hyperentanglement purification and hyperdistillation with linear optics,” Opt. Express 23, 9284–9294 (2015).
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T. J. Wang, C. Cao, and C. Wang, “Linear-optical implementation of hyperdistillation from photon loss,” Phys. Rev. A 89, 052303 (2014).
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Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. 109, 160504 (2012).
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Chen, M. C.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518, 516–519 (2015).
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Z. Y. Xue, Z. Q. Yin, Y. Chen, Z. D. Wang, and S. L. Zhu, “Topological quantum memory interfacing atomic and superconducting qubits,” Sci. China Phys. Mech. Astron. 59, 660301 (2016).
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Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
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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 497, 86–90 (2013).
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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 466, 730–734 (2010).
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Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
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L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. G. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
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[Crossref]

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[Crossref]

Sci. Rep. (2)

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1 (a) A one-sided cavity-NV-center system. The optical cavity consists of two concave mirrors. The bottom mirror is 100% reflective and the top mirror is partially reflective. (b) The optical transitions between the ground states (|E0〉 |∓1〉) and the excited state |A2〉. The photon state |L〉 corresponds to σ+ = 1 and the photon state |R〉 corresponds to σ = −1.
Fig. 2
Fig. 2 The cavity mode decay rate λ vs the Purcell factor FP in the balance condition of a one-sided cavity-NV-center system.
Fig. 3
Fig. 3 Schematic diagram for the robust hyper-CPF gate operating on the spatial-mode and polarization DOFs of a two-photon system in the balance condition. NV1 and NV2 represent two one-sided cavity-NV-center systems with reflection coefficient r. X1 and X2 represent two half-wave plates, which can perform the bit-flip operations σ x P = | R L | + | L R | on the polarization DOF of a photon. CPBSk (k = 1, 2, 3, 4) represents a polarizing beam splitter in the circular basis, which can transmit the photon in polarization state |R〉 and reflect the photon in polarization state |L〉. DL represents a time-delay device, which can make |R〉 arrive simultaneously with |L〉. WFC represents a waveform corrector, which can map |i2〉 to r|i2〉. i1 and i2 denote two spatial modes of photon i (i = a, b).
Fig. 4
Fig. 4 Schematic diagram for the unbalanced beam splitter. BS represents a 50:50 beam splitter. Rθ represents a wave plate, which is used to perform a phase shift on a spatial mode of a photon. D represents a photon detector.
Fig. 5
Fig. 5 The reflection cofficient r of the one-sided cavity-NV-center system vs the Purcell factor FP in the balance condition.
Fig. 6
Fig. 6 Efficiency of the robust hyper-CPF gate vs the Purcell factor FP in the balance condition.

Equations (10)

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d a ^ d t = [ i ( ω c ω ) + η 2 + κ 2 ] a ^ g σ ^ η a ^ in , d σ ^ d t = [ i ( ω e ω ) + γ 2 ] σ ^ g σ ^ z a ^ ,
r ( ω ) = a ^ out a ^ in = [ i ( ω e ω ) + γ 2 ] [ i ( ω c ω ) η 2 + κ 2 ] + g 2 [ i ( ω e ω ) + γ 2 ] [ i ( ω c ω ) + η 2 + κ 2 ] + g 2 .
| L , 1 r | L , 1 , | L , + 1 r | L , + 1 , | R , 1 r | R , 1 , | R , + 1 r | R , + 1 .
| Ψ a e 1 = 1 2 { γ 1 [ | 1 e 1 ( α 1 | R + β 1 | L ) a + | + 1 e 1 ( α 1 | R β 1 | L ) a ] | a 1 + δ 1 [ | 1 e 1 ( α 1 | R + β 1 | L ) a + | + 1 e 1 ( α 1 | R + β 1 | L ) a ] | a 2 } .
| Ψ a e 1 e 2 = 1 2 { [ | 1 e 1 ( γ 1 | a 1 δ 1 | a 2 ) + | + 1 e 1 ( γ 1 | a 1 + δ 1 | a 2 ) ] [ | 1 e 2 ( α 1 | R + β 1 | L ) a + | + 1 e 2 ( α 1 | R β 1 | L ) a ] } .
| Ψ a b e 1 e 2 = [ | 1 e 1 δ | a 2 ( γ 2 | b 1 δ 2 | b 2 ) + | + 1 e 1 γ 1 | a 1 ( γ 2 | b 1 + δ 2 | b 2 ) ] [ | 1 e 2 α 1 | R a ( α 2 | R + β 2 | L ) b + | + 1 e 2 β 1 | L a ( α 2 | R β 2 | L ) b ] .
| ψ a b = [ γ 1 | a 1 ( γ 2 | b 1 + δ 2 | b 2 ) + δ 1 | a 2 ( γ 2 | b 1 δ 2 | b 2 ) ] [ α 1 | R a ( α 2 | R + β 2 | L ) b + β 1 | L a ( α 2 | R β 2 | L ) b ] .
| Ψ a e 1 = 1 2 { γ 1 [ | 1 e 1 ( r 0 α 1 | R + r β 1 | L ) a + | + 1 e 1 ( r α 1 | R + r 0 β 1 | L ) a ] | a 1 + δ 1 [ | 1 e 1 ( α 1 | R + β 1 | L ) a + | + 1 e 1 ( α 1 | R + β 1 | L ) a ] | a 2 } ,
| Ψ a e 1 = 1 2 { r γ 1 [ | 1 e 1 ( α 1 | R + β 1 | L ) a + | + 1 e 1 ( α 1 | R + β 1 | L ) a ] | a 1 + δ 1 [ | 1 e 1 ( α 1 | R + β 1 | L ) a + | + 1 e 1 ( α 1 | R + β 1 | L ) a ] | a 2 } ,
| Ψ a e 1 = 1 2 { γ 1 [ | 1 e 1 ( α 1 | R + β 1 | L ) a + | + 1 e 1 ( α 1 | R + β 1 | L ) a ] | a 1 + δ 1 [ | 1 e 1 ( α 1 | R + β 1 | L ) a + | + 1 e 1 ( α 1 | R + β 1 | L ) a ] | a 2 } .

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