Error-detected three-photon hyperparallel Toffoli gate with state-selective reflection

Abstract

We present an error-detected hyperparallel Toffoli (hyper-Toffoli) gate for a three-photon system based on the interface between polarized photon and cavity-nitrogen-vacancy (NV) center system. This hyper-Toffoli gate can be used to perform double Toffoli gate operations simultaneously on both the polarization and spatial-mode degrees of freedom (DoFs) of a three-photon system with a low decoherence, shorten operation time, and less quantum resources required, in compared with those on two independent three-photon systems in one DoF only. As the imperfect cavity-NV-center interactions are transformed into the detectable failures rather than infidelity based on the heralding mechanism of detectors, a near-unit fidelity of the quantum hyper-Toffoli gate can be implemented. By recycling the procedures, the efficiency of our protocol for the hyper-Toffoli gate is improved further. Meanwhile, the evaluation of gate performance with achieved experiment parameters shows that it is feasible with current experimental technology and provides a promising building block for quantum compute.

Graphical abstract

Keywords

hyperparallel Toffoli gate / photon system / quantum information processing

References

[1] M. A. Nielsen , I. Chuang , L. K. Grover . Quantum computation and quantum information. Am. J. Phys., 2002, 70( 5): 558

[2] L. X. Liang , Y. Y. Zheng , Y. X. Zhang , M. Zhang . Error-detected N-photon cluster state generation based on the controlled-phase gate using a quantum dot in an optical microcavity. Front. Phys., 2020, 15( 2): 21601

[3] T. Li , G. L. Long . Quantum secure direct communication based on single-photon Bell-state measurement. New J. Phys., 2020, 22( 6): 063017

[4] Z. D. Ye , D. Pan , Z. Sun , C. G. Du , L. G. Yin , G. L. Long . Generic security analysis framework for quantum secure direct communication. Front. Phys., 2021, 16( 2): 21503

[5] P. S. Yan , L. Zhou , W. Zhong , Y. B. Sheng . Measurement-based entanglement purification for entangled coherent states. Front. Phys., 2022, 17( 2): 21501

[6] C. Wang . Quantum secure direct communication: Intersection of communication and cryptography. Fundam. Res., 2021, 1( 1): 91

[7] P. Wang , C. Q. Yu , Z. X. Wang , R. Y. Yuan , F. F. Du , B. C. Ren . Hyperentanglement-assisted hyperdistillation for hyper-encoding photon system. Front. Phys., 2022, 17( 3): 31501

[8] P. W. Shor . Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev., 1999, 41( 2): 303

[9] L. K. Grover . Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett., 1997, 79( 2): 325

[10] M. AbuGhanem , A. H. Homid , M. Abdel-Aty . Cavity control as a new quantum algorithms implementation treatment. Front. Phys., 2018, 13( 1): 130303

[11] X. D. Cai , D. Wu , Z. E. Su , M. C. Chen , X. L. Wang , L. Li , N. L. Liu , C. Y. Lu , J. W. Pan . Entanglement-based machine learning on a quantum computer. Phys. Rev. Lett., 2015, 114( 11): 110504

[12] J. Allcock , S. Y. Zhang . Quantum machine learning. Natl. Sci. Rev., 2019, 6( 1): 26

[13] X. L. Ouyang , X. Z. Huang , Y. K. Wu , W. G. Zhang , X. Wang , H. L. Zhang , L. He , X. Y. Chang , L. M. Duan . Experimental demonstration of quantum-enhanced machine learning in a nitrogen-vacancy-center system. Phys. Rev. A, 2020, 101( 1): 012307

[14] D. R. Chong , M. Kim , J. Ahn , H. Jeong . Machine learning identification of symmetrized base states of Rydberg atoms. Front. Phys., 2022, 17( 1): 12504

[15] W. Q. Liu , H. R. Wei . Optimal synthesis of the Fredkin gate in a multilevel system. New J. Phys., 2020, 22( 6): 063026

[16] W. Q. Liu , H. R. Wei , L. C. Kwek . Low-cost Fredkin gate with auxiliary space. Phys. Rev. A, 2020, 14( 5): 054057

[17] V. V. Shende , I. L. Markov , S. S. Bullock . Minimal universal two-qubit controlled-NOT-based circuits. Phys. Rev. A, 2004, 69( 6): 062321

[18] T. C. Ralph , K. J. Resch , A. Gilchrist . Efficient Toffoli gates using qudits. Phys. Rev. A, 2007, 75( 2): 022313

[19] I. Radu , T. P. Spiller , W. J. Munro . Generalized Toffoli gates using qudit catalysis. Phys. Rev. A, 2009, 80( 1): 012313

[20] N. K. Yu , R. Y. Duan , M. S. Ying . Five two-qubit gates are necessary for implementing the Toffoli gate. Phys. Rev. A, 2013, 88( 1): 010304

[21] J. Fiurášek . Linear-optics quantum Toffoli and Fredkin gates. Phys. Rev. A, 2006, 73( 6): 062313

[22] M. Soeken , D. M. Miller , R. Drechsler . Quantum circuits employing roots of the Pauli matrices. Phys. Rev. A, 2013, 88( 4): 042322

[23] A. Fedorov , L. Steffen , M. Baur , M. P. da Silva , A. Wallraff . Implementation of a Toffoli gate with superconducting circuits. Nature, 2012, 481( 7380): 170

[24] S. E. Rasmussen , K. Groenland , R. Gerritsma , K. Schoutens , N. T. Zinner . Single-step implementation of high-fidelity n-bit Toffoli gatess. Phys. Rev. A, 2020, 101( 2): 022308

[25] S. Daraeizadeh , S. P. Premaratne , N. Khammassi , X. Song , M. Perkowski , A. Y. Matsuura . Machine learning-based three-qubit gate design for the Toffoli gate and parity check in transmon systems. Phys. Rev. A, 2020, 102( 1): 012601

[26] H. R. Wei , F. G. Deng . Compact quantum gates on electron-spin qubits assisted by diamond nitrogen vacancy centers inside cavities. Phys. Rev. A, 2013, 88( 4): 042323

[27] H. R. Wei , F. G. Deng . Scalable quantum computing based on stationary spin qubits in coupled quantum dots inside double-sided optical microcavities. Sci. Rep., 2015, 4( 1): 7551

[28] H. R. Wei , F. G. Deng . Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities. Opt. Express, 2014, 22( 1): 593

[29] G. Z. Song , J. L. Guo , Q. Liu , H. R. Wei , G. L. Long . Heralded quantum gates for hybrid systems via waveguide-mediated photon scattering. Phys. Rev. A, 2021, 104( 1): 012608

[30] T. Monz , K. Kim , W. Hänsel , M. Riebe , A. S. Villar , P. Schindler , M. Chwalla , M. Hennrich , R. Blatt . Realization of the quantum Toffoli gate with trapped ions. Phys. Rev. Lett., 2009, 102( 4): 040501

[31] D. Solenov , S. E. Economou , T. L. Reinecke . Fast two-qubit gates for quantum computing in semiconductor quantum dots using a photonic microcavity. Phys. Rev. B, 2013, 87( 3): 035308

[32] 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 , A. G. White . Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys., 2009, 5( 2): 134

[33] E. O. Kiktenko , A. S. Nikolaeva , P. Xu , G. V. Shlyapnikov , A. K. Fedorov . Scalable quantum computing with qudits on a graph. Phys. Rev. A, 2020, 101( 2): 022304

[34] T. Li , G. L. Long . Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities. Phys. Rev. A, 2016, 94( 2): 022343

[35] Y. H. Han , C. Cao , L. Fan , R. Zhang . Heralded high-fidelity quantum hyper-CNOT gates assisted by charged quantum dots inside single-sided optical microcavities. Opt. Express, 2021, 29( 13): 20045

[36] F. F. Du , Z. R. Shi . Robust hybrid hyper-controlled-not gates assisted by an input−output process of low-Q cavities. Opt. Express, 2019, 27( 13): 17493

[37] H. R. Wei , G. L. Long . Universal photonic quantum gates assisted by ancilla diamond nitrogen-vacancy centers coupled to resonators. Phys. Rev. A, 2015, 91( 3): 032324

[38] T. J. Wang , Y. Zhang , C. Wang . Universal hybrid hyper-controlled quantum gates assisted by quantum dots in optical double-sided microcavities. Laser Phys. Lett., 2014, 11( 2): 025203

[39] H. R. Wei , F. G. Deng , G. L. Long . Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities. Opt. Express, 2016, 24( 16): 18619

[40] S. H. Ru , Y. L. Wang , M. An , F. R. Wang , P. Zhang , F. L. Li . Realization of a deterministic quantum Toffoli gate with a single photon. Phys. Rev. A, 2021, 103( 2): 022606

[41] 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 , J. Wrachtrup . Room-temperature coherent coupling of single spins in diamond. Nat. Phys., 2006, 2( 6): 408

[42] G. D. Fuchs , V. V. Dobrovitski , D. M. Toyli , F. J. Heremans , D. D. Awschalom . Gigahertz dynamics of a strongly driven single quantum spin. Science, 2009, 326( 5959): 1520

[43] D. Englund , B. Shields , K. Rivoire , F. Hatami , J. Vučković , H. Park , M. D. Lukin . Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity. Nano Lett., 2010, 10( 10): 3922

[44] J. Zhang , D. Suter . Experimental Protection of Two-Qubit Quantum Gates against Environmental Noise by Dynamical Decoupling. Phys. Rev. Lett., 2015, 115( 11): 110502

[45] L. Robledo , L. Childress , H. Bernien , B. Hensen , P. F. A. Alkemade , R. Hanson . High-fidelity projective readout of a solid-state spin quantum register. Nature, 2011, 477( 7366): 574

[46] M. V. G. Dutt , L. Childress , L. Jiang , E. Togan , J. Maze , F. Jelezko , A. S. Zibrov , P. R. Hemmer , M. D. Lukin . Quantum register based on individual electronic and nuclear spin qubits in diamond. Science, 2007, 316( 5829): 1312

[47] F. Shi , X. Rong , N. Xu , Y. Wang , J. Wu , B. Chong , X. Peng , J. Kniepert , R. S. Schoenfeld , W. Harneit , M. Feng , J. Du . Room-temperature implementation of the Deutsch−Jozsa algorithm with a single electronic spin in diamond. Phys. Rev. Lett., 2010, 105( 4): 040504

[48] 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 , V. V. Dobrovitski . Decoherence-protected quantum gates for a hybrid solid-state spin register. Nature, 2012, 484( 7392): 82

[49] S. Arroyo-Camejo , A. Lazariev , S. W. Hell , G. Balasubramanian . Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin. Nat. Commun., 2014, 5( 1): 4870

[50] C. Zu , W. B. Wang , L. He , W. G. Zhang , C. Y. Dai , F. Wang , L. M. Duan . Experimental realization of universal geometric quantum gates with solid-state spins. Nature, 2014, 514( 7520): 72

[51] 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 , M. D. Lukin . Quantum entanglement between an optical photon and a solid-state spin qubit. Nature, 2010, 466( 7307): 730

[52] H. Kosaka , N. Niikura . Entangled absorption of a single photon with a single spin in diamond. Phys. Rev. Lett., 2015, 114( 5): 053603

[53] H. Bernien , B. Hensen , W. Pfaff , G. Koolstra , M. S. Blok , L. Robledo , T. H. Taminiau , M. Markham , D. J. Twitchen , L. Childress , R. Hanson . Heralded entanglement between solid-state qubits separated by three metres. Nature, 2013, 497( 7447): 86

[54] B. C. Ren , F. G. Deng . Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities. Laser Phys. Lett., 2013, 10( 11): 115201

[55] T. J. Wang , C. Wang . Universal hybrid three-qubit quantum gates assisted by a nitrogen-vacancy center coupled with a whispering-gallery-mode microresonator. Phys. Rev. A, 2014, 90( 5): 052310

[56] C. Wang , Y. Zhang , R. Z. Jiao , G. S. Jin . Universal quantum controlled phase gate on photonic qubits based on nitrogen vacancy centers and microcavity resonators. Opt. Express, 2013, 21( 16): 19252

[57] F. F. Du , Y. T. Liu , Z. R. Shi , Y. X. Liang , J. Tang , J. Liu . Efficient hyperentanglement purification for three-photon systems with the fidelity-robust quantum gates and hyperentanglement link. Opt. Express, 2019, 27( 19): 27046

[58] Q. Chen , W. Yang , M. Feng , J. Du . Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators. Phys. Rev. A, 2011, 83( 5): 054305

[59] M. O. Scully M. S. Zubairy, Quantum Optics, Cambridge University Press, 1997

[60] C. Y. Hu , W. J. Munro , J. G. Rarity . Deterministic photon entangler using a charged quantum dot inside a microcavity. Phys. Rev. B, 2008, 78( 12): 125318

[61] J. H. An , M. Feng , C. H. Oh . Quantum-information processing with a single photon by an input−output process with respect to low-Q cavities. Phys. Rev. A, 2009, 79( 3): 032303

[62] B. C. Pursley , S. G. Carter , M. K. Yakes , A. S. Bracker , D. Gammon . Picosecond pulse shaping of single photons using quantum dots. Nat. Commun., 2018, 9( 1): 115

[63] R. Albrecht , A. Bommer , C. Deutsch , J. Reichel , C. Becher . Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity. Phys. Rev. Lett., 2013, 110( 24): 243602

[64] 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 , M. Lonc̆ar . Integrated diamond networks for quantum nanophotonics. Nano Lett., 2012, 12( 3): 1578

[65] J. Teissier , A. Barfuss , P. Appel , E. Neu , P. Maletinsky . Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator. Phys. Rev. Lett., 2014, 113( 2): 020503

[66] K. M. C. Fu , C. Santori , P. E. Barclay , L. J. Rogers , N. B. Manson , R. G. Beausoleil . Observation of the dynamic Jahn−Teller effect in the excited states of nitrogen-vacancy centers in diamond. Phys. Rev. Lett., 2009, 103( 25): 256404

[67] L. C. Bassett , F. J. Heremans , C. G. Yale , B. B. Buckley , D. D. Awschalom . Electrical tuning of single nitrogen-vacancy center optical transitions enhanced by photoinduced fields. Phys. Rev. Lett., 2011, 107( 26): 266403

[68] P. Siyushev , H. Pinto , M. Vörös , A. Gali , F. Jelezko , J. Wrachtrup . Optically controlled switching of the charge state of a single nitrogen-vacancy center in diamond at cryogenic temperatures. Phys. Rev. Lett., 2013, 110( 16): 167402

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