基于多光子纠缠技术的多方量子任务研究

 随着量子技术的发展，量子互联已成为当前量子信息科学研究的新趋势，量 子通信、量子模拟、量子计算等量子信息处理任务最终都将在量子互联网络中开 展。量子计算是利用量子态叠加原理和量子纠缠来实现的基于量子物理体系的信 息处理过程。Deutsch 算法和 Shor 算法的提出展示出了量子计算的优越性。目前 在超导和光子系统中已经证明了量子优势。然而，制备出具有数千个或更多量子 比特的量子处理器目前依旧是一个巨大的挑战，而解决这个问题的一条路径是实 现基于量子网络的分布式量子计算，它可以连接多个网络节点间的量子资源，将 复杂的量子计算任务分发给多方进行简化，从而提高量子计算的效率和计算能力。 这衍生出了盲分布式量子计算、多方量子私密共享、分布式量子编码解码等诸多 新的量子信息处理任务。而完成此类量子计算任务的关键问题是如何在量子网络 的不同节点之间相干地共享或者传递量子态和逻辑门操作。量子隐形传态作为传 递量子态的隐形传输过程目前研究较多，而作为量子逻辑门隐形传输过程的分布 式量子逻辑门目前只在中性原子、线性光学、离子阱、超导等实验系统实现了两 比特的实验演示，有着更快执行速度、更高的保真度、更节省资源等优势的多比 特分布式量子门操作亟待研究。

本文的主要工作是利用多光子纠缠技术搭建量子网络雏形，以控制非门为例 研究多比特分布式量子门在不同网络节点间的分享并进行相关的实验演示。本文 首次提出利用 N 比特 GHZ 纠缠态来实现多方间分布式量子控制非门，并基于多光 子纠缠实验平台，引入光子的路径态作为辅助的 GHZ 纠缠态首次完成了三比特分 布式控制非门方案的实验验证，我们利用量子过程层析的方法表征了分布式控制 非门的性能，得到该三比特分布式控制非门的保真度达 0.861±0.004。最后，我们 基于三比特分布式控制非门进行了比特翻转码和相位翻转码的分布式量子编码工 作，得到平均保真度为 0.828±0.019。

[1] HWANG W Y. Quantum Key Distribution with High Loss: Toward Global Secure Communication[J]. Phys. Rev. Lett., 2003, 91(5): 057901.
[2] LO H K, CURTY M, QI B. Measurement-Device-Independent Quantum Key Distribution[J].Phys. Rev. Lett., 2012, 108(13): 130503.
[3] LIAO S K, CAI W Q, LIU W Y, et al. Satellite-to-ground quantum key distribution[J]. Nature,2017, 549(7670): 43-47.
[4] BENNETT C H, BRASSARD G, CRéPEAU C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. Phys. Rev. Lett., 1993, 70(13):1895-1899.
[5] ZHAO Z, CHEN Y A, ZHANG A N, et al. Experimental demonstration of five-photon entanglement and open-destination teleportation[J]. Nature, 2004, 430(6995): 54-58.
[6] SCHIERMEIER Q. The philosopher of photons[J]. Nature, 2005, 434(7037): 1066-1066.
[7] ZHONG H S, DENG Y H, QIN J, et al. Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light[J]. Phys. Rev. Lett., 2021, 127: 180502.
[8] LU C Y, BROWNE D E, YANG T, et al. Demonstration of a Compiled Version of Shor’s Quantum Factoring Algorithm Using Photonic Qubits[J]. Phys. Rev. Lett., 2007, 99(25): 250504.
[9] ARUTE F, ARYA K, BABBUSH R, et al. Quantum supremacy using a programmable superconducting processor.[J]. Nature, 2019, 574(7779): 505-510.
[10] ZHONG H S, WANG H, DENG Y H, et al. Quantum computational advantage using photons[J]. Science, 2020, 370(6523): 1460-1463.
[11] POLITI A, MATTHEWS J C F, O’BRIEN J L. Shor’s Quantum Factoring Algorithm on a Photonic Chip[J]. Science, 2009, 325(5945): 1221-1221.
[12] PORRAS D, CIRAC J I. Effective Quantum Spin Systems with Trapped Ions[J]. Phys. Rev.Lett., 2004, 92(20): 207901.
[13] BLATT R, ROOS C F. Quantum simulations with trapped ions[J]. Nat. Phys., 2012, 8(4):277-284.
[14] ZHANG J, PAGANO G, HESS P W, et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator.[J]. Nature, 2017, 551(7682): 601-604.
[15] KASEVICH M, CHU S. Atomic interferometry using stimulated Raman transitions[J]. Phys.Rev. Lett., 1991, 67(2): 181-184.
[16] WEISS Y, CHU. Precision measurement of the photon recoil of an atom using atomic interferometry.[J]. Phys. Rev. Lett., 1993, 70(18): 2706-2709.
[17] GALINDO A, MARTíN-DELGADO M A. Information and computation: Classical and quantum aspects[J]. Rev. Mod. Phys., 2002, 74(2): 347-423.
[18] NIELSEN M A, CHUANG I L. Quantum Computation and Quantum Information: 10th Anniversary Edition[M]. Cambridge University Press, 2010.
[19] GONG M, WANG S, ZHA C, et al. Quantum walks on a programmable two-dimensional 62-qubit superconducting processor[J]. Science, 2021, 372(6545): 948-952.
[20] WU Y, BAO W S, CAO S, et al. Strong Quantum Computational Advantage Using a Superconducting Quantum Processor[J]. Phys. Rev. Lett., 2021, 127(18): 180501.
[21] ZHU Q, CAO S, CHEN F, et al. Quantum computational advantage via 60-qubit 24-cycle random circuit sampling[J]. Science Bulletin, 2022, 67(3): 240-245.
[22] MADSEN L S, LAUDENBACH F, ASKARANI M F, et al. Quantum computational advantage with a programmable photonic processor[J]. Nature, 2022, 606(7912): 75-81.
[23] KIMBLE H J. The quantum internet[J]. Nature, 2008, 453(7198): 1023-1030.
[24] MONROE C, RAUSSENDORF R, RUTHVEN A, et al. Large-scale modular quantumcomputer architecture with atomic memory and photonic interconnects[J]. Phys. Rev. A, 2014,89(2): 022317.
[25] BOUWMEESTER D, PAN J W, MATTLE K, et al. Experimental quantum teleportation[J].Nature, 1997, 390(6660): 575-579.
[26] ZHANG Q, GOEBEL A, WAGENKNECHT C, et al. Experimental quantum teleportation of a two-qubit composite system[J]. Nat. Phys., 2006, 2(10): 678-682.
[27] WANG X L, CAI X D, SU Z E, et al. Quantum teleportation of multiple degrees of freedom of a single photon[J]. Nature, 2015, 518(7540): 516-519.
[28] LUO Y H, ZHONG H S, ERHARD M, et al. Quantum Teleportation in High Dimensions[J].Phys. Rev. Lett., 2019, 123(7): 070505.
[29] URSIN R, JENNEWEIN T, ASPELMEYER M, et al. Quantum teleportation across the Danube[J]. Nature, 2004, 430(7002): 849-849.
[30] REN J G, XU P, YONG H L, et al. Ground-to-satellite quantum teleportation[J]. Nature, 2017,549(7670): 70-73.
[31] KNILL E, LAFLAMME R, MILBURN G J. A scheme for efficient quantum computation with linear optics[J]. Nature, 2001, 409(6816): 46-52.
[32] O’BRIEN J L, PRYDE G J, WHITE A G, et al. Demonstration of an all-optical quantum controlled-NOT gate[J]. Nature, 2003, 426(6964): 264-267.
[33] HUANG Y F, REN X F, ZHANG Y S, et al. Experimental Teleportation of a Quantum Controlled-NOT Gate[J]. Phys. Rev. Lett., 2004, 93(24): 240501.
[34] GAO W B, GOEBEL A M, LU C Y, et al. Teleportation-based realization of an optical quantum two-qubit entangling gate[J]. Proceedings of the National Academy of Sciences, 2010, 107(49):20869-20874.
[35] CHOU K S, BLUMOFF J Z, WANG C S, et al. Deterministic teleportation of a quant um gate between two logical qubits[J]. Nature, 2018, 561(7723): 368-373.
[36] WAN Y, KIENZLER D, ERICKSON S D, et al. Quantum gate teleportation between separated qubits in a trapped-ion processor[J]. Science, 2019, 364(6443): 875-878.
[37] DAISS S, LANGENFELD S, WELTE S, et al. A quantum-logic gate between distant quantum network modules[J]. Science, 2021, 371(6529): 614-617.
[38] MONZ T, KIM K, HäNSEL W, et al. Realization of the Quantum Toffoli Gate with Trapped Ions[J]. Phys. Rev. Lett., 2009, 102(4): 040501.
[39] REED M D, DICARLO L, NIGG S E, et al. Realization of three-qubit quantum error correction with superconducting circuits[J]. Nature, 2012, 482(7385): 382-385.
[40] KIM Y, MORVAN A, NGUYEN L B, et al. High-fidelity three-qubit iToffoli gate for fixed frequency superconducting qubits[J]. Nat. Phys., 2022, 18(7): 783-788.
[41] LEVINE H, KEESLING A, SEMEGHINI G, et al. Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms[J]. Phys. Rev. Lett., 2019, 123(17): 170503.
[42] KHAZALI M, MøLMER K. Fast Multiqubit Gates by Adiabatic Evolution in Interacting Excited-State Manifolds of Rydberg Atoms and Superconducting Circuits[J]. Phys. Rev. X, 2020,10(2): 021054.
[43] TAKEDA K, NOIRI A, NAKAJIMA T, et al. Quantum error correction with silicon spin qubits[J]. Nature, 2022, 608(7924): 682-686.
[44] EINSTEIN A, PODOLSKY B, ROSEN N. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?[J]. Phys. Rev., 1935, 47(10): 777-780.
[45] ASPECT A, GRANGIER P, ROGER G. Experimental Realization of Einstein-Podolsky-Rosen Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities[J]. Phys. Rev. Lett., 1982,49(2): 91-94.
[46] GILCHRIST A, LANGFORD N K, NIELSEN M A. Distance measures to compare real and ideal quantum processes[J]. Phys. Rev. A, 2005, 71(6): 062310.
[47] GüHNE O, TóTH G. Entanglement detection[J]. Phys. Rep., 2009, 474(1): 1-75.
[48] MIıFMMODE \CHECKC\ELSE č\FIUDA M, SEDLáK M, STRAKA I, et al. Efficient Experimental Estimation of Fidelity of Linear Optical Quantum Toffoli Gate[J]. Phys. Rev. Lett.,2013, 111(16): 160407.
[49] RU S, WANG Y, AN M, et al. Realization of a deterministic quantum Toffoli gate with a single photon[J]. Phys. Rev. A, 2021, 103: 022606.
[50] HUANG H L, BAO W S, LI T, et al. Deterministic linear optical quantum Toffoli gate[J]. Phys.Lett. A, 2017, 381(33): 2673-2676.
[51] WEI H R, DENG F G, LONG G L. Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities[J]. Opt. Express, 2016,24(16): 18619-18630.
[52] WANG G Y, LIU Q, WEI H R, et al. Universal quantum gates for photon-atom hybrid systems assisted by bad cavities[J]. Sci. Rep., 2016, 6(1): 24183.
[53] KWIAT P G, MATTLE K, WEINFURTER H, et al. New High-Intensity Source of PolarizationEntangled Photon Pairs[J]. Phys. Rev. Lett., 1995, 75(24): 4337-4341.
[54] BOUWMEESTER D, PAN J W, DANIELL M, et al. Observation of Three-Photon Greenberger Horne-Zeilinger Entanglement[J]. Phys. Rev. Lett., 1999, 82(7): 1345-1349.
[55] PAN J W, SIMON C, BRUKNER ff, et al. Entanglement purification for quantum communication[J]. Nature, 2001, 410(6832): 1067-1070.
[56] LU C Y, ZHOU X Q, GüHNE O, et al. Experimental entanglement of six photons in graph states[J]. Nat. Phys., 2007, 3(2): 91-95.
[57] YAO X C, WANG T X, XU P, et al. Observation of eight-photon entanglement[J]. Nat. Photonics, 2012, 6(4): 225-228.
[58] WANG X L, CHEN L K, LI W, et al. Experimental Ten-Photon Entanglement[J]. Phys. Rev.Lett., 2016, 117(21): 210502.
[59] ZHONG H S, LI Y, LI W, et al. 12-Photon Entanglement and Scalable Scattershot Boson Sampling with Optimal Entangled-Photon Pairs from Parametric Down-Conversion[J]. Phys.Rev. Lett., 2018, 121(25): 250505.
[60] BROADBENT A, FITZSIMONS J, KASHEFI E. Universal Blind Quantum Computation[C]//2009 50th Annual IEEE Symposium on Foundations of Computer Science. 2009: 517-526.
[61] HUANG H L, ZHAO Q, MA X, et al. Experimental Blind Quantum Computing for a Classical Client[J]. Phys. Rev. Lett., 2017, 119(5): 050503.
[62] RAUSSENDORF R, BRIEGEL H J. A One-Way Quantum Computer[J]. Phys. Rev. Lett., 2001,86(22): 5188-5191.
[63] WALTHER P, RESCH K J, RUDOLPH T, et al. Experimental one-way quantum computing[J].Nature, 2005, 434(7030): 169-176.
[64] CHEN Y A, ZHANG A N, ZHAO Z, et al. Experimental Quantum Secret Sharing and ThirdMan Quantum Cryptography[J]. Phys. Rev. Lett., 2005, 95(20): 200502.
[65] LU H, ZHANG Z, CHEN L K, et al. Secret Sharing of a Quantum State[J]. Phys. Rev. Lett.,2016, 117(3): 030501.
[66] URSIN R, TIEFENBACHER F, SCHMITT-MANDERBACH T, et al. Entanglement-based quantum communication over 144 km[J]. Nat. Phys., 2007, 3(7): 481-486.
[67] KWIAT P G, WAKS E, WHITE A G, et al. Ultrabright source of polarization-entangled photons[J]. Phys. Rev. A, 1999, 60(2): R773-R776.
[68] TAKEUCHI S. Beamlike twin-photon generation by use of type II parametric downconversion[J]. Opt. Lett., 2001, 26(11): 843-845.
[69] KIM Y H. Quantum interference with beamlike type-II spontaneous parametric downconversion[J]. Phys. Rev. A, 2003, 68(1): 013804.
[70] SIMON C, BOUWMEESTER D. Theory of an Entanglement Laser[J]. Phys. Rev. Lett., 2003,91(5): 053601.
[71] HONG C K, OU Z Y, MANDEL L. Measurement of subpicosecond time intervals between two photons by interference[J]. Phys. Rev. Lett., 1987, 59(18): 2044-2046.
[72] ZHAO Z, YANG T, CHEN Y A, et al. Experimental Violation of Local Realism by Four-Photon Greenberger-Horne-Zeilinger Entanglement[J]. Phys. Rev. Lett., 2003, 91(18): 180401.
[73] ŻUKOWSKI M. Bell theorem involving all settings of measuring apparatus[J]. Phys. Lett. A,1993, 177(4): 290-296.
[74] KWIAT P G, WEINFURTER H. Embedded Bell-state analysis[J]. Phys. Rev. A, 1998, 58(4):R2623-R2626.
[75] BLINOV B B, MOEHRING D L, DUAN L M, et al. Observation of entanglement between asingle trapped atom and a single photon[J]. Nature, 2004, 428(6979): 153-157.
[76] WOOTTERS W K, ZUREK W H. A single quantum cannot be cloned[J]. Nature, 1982, 299(5886): 802-803.
[77] MAO Y L, MA Z H, JIN R B, et al. Error-Disturbance Trade-off in Sequential Quantum Measurements[J]. Phys. Rev. Lett., 2019, 122(9): 090404.
[78] LI Z D, YUAN X, YIN X F, et al. Experimental random-party entanglement distillation via weak measurement[J]. Phys. Rev. Res., 2020, 2(2): 023047.
[79] MAO Y L, LI Z D, STEFFINLONGO A, et al. Recycling nonlocality in quantum star networks[J]. Phys. Rev. Res., 2023, 5(1): 013104.
[80] JAMES D F V, KWIAT P G, MUNRO W J, et al. Measurement of qubits[J]. Phys. Rev. A,2001, 64(5): 052312.
[81] ALTEPETER J B, JEFFREY E R, KWIAT P G. Photonic State Tomography[J]. Adv. At. Mol.Opt. Phys., 2005, 52: 105-159.
[82] HOFMANN H F. Complementary Classical Fidelities as an Efficient Criterion for the Evaluation of Experimentally Realized Quantum Operations[J]. Phys. Rev. Lett., 2005, 94(16):160504.
[83] HOFMANN H F, OKAMOTO R, TAKEUCHI S. Analysis of an experimental quantum logic gate by complementary classical operations[J]. Mod. Phys. Lett. A, 2006, 21(24): 1837-1850.
[84] CHUANG I L, NIELSEN M A. Prescription for experimental determination of the dynamics of a quantum black box[J]. J. Mod. Opt., 1997, 44(11-12): 2455-2467.
[85] ALTEPETER J B, BRANNING D, JEFFREY E, et al. Ancilla-Assisted Quantum Process Tomography[J]. Phys. Rev. Lett., 2003, 90(19): 193601.
[86] POYATOS J F, CIRAC J I, ZOLLER P. Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate[J]. Phys. Rev. Lett., 1997, 78(2): 390-393.
[87] CHILDS A M, CHUANG I L, LEUNG D W. Realization of quantum process tomography in NMR[J]. Phys. Rev. A, 2001, 64(1): 012314.
[88] DE MARTINI F, MAZZEI A, RICCI M, et al. Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single-qubit device[J]. Phys. Rev. A,2003, 67(6): 062307.
[89] O’BRIEN J L, PRYDE G J, GILCHRIST A, et al. Quantum Process Tomography of a Controlled-NOT Gate[J]. Phys. Rev. Lett., 2004, 93(8): 080502.
[90] MITCHELL M W, ELLENOR C W, SCHNEIDER S, et al. Diagnosis, Prescription, and Prognosis of a Bell-State Filter by Quantum Process Tomography[J]. Phys. Rev. Lett., 2003, 91(12):120402.
[91] NEELEY M, ANSMANN M, BIALCZAK R C, et al. Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state[J]. Nat. Phys., 2008, 4(7): 523-526.
[92] CHOW J M, GAMBETTA J M, TORNBERG L, et al. Randomized Benchmarking and Process Tomography for Gate Errors in a Solid-State Qubit[J]. Phys. Rev. Lett., 2009, 102(9): 090502.
[93] BIALCZAK R C, ANSMANN M, HOFHEINZ M, et al. Quantum process tomography of a universal entangling gate implemented with Josephson phase qubits[J]. Nat. Phys., 2010, 6(6):409-413.
[94] YAMAMOTO T, NEELEY M, LUCERO E, et al. Quantum process tomography of two-qubit controlled-Z and controlled-NOT gates using superconducting phase qubits[J]. Phys. Rev. B,2010, 82(18): 184515.
[95] CHOW J M, CóRCOLES A D, GAMBETTA J M, et al. Simple All-Microwave Entangling Gate for Fixed-Frequency Superconducting Qubits[J]. Phys. Rev. Lett., 2011, 107(8): 080502.
[96] RIEBE M, KIM K, SCHINDLER P, et al. Process Tomography of Ion Trap Quantum Gates[J].Phys. Rev. Lett., 2006, 97(22): 220407.
[97] HANNEKE D, HOME J P, JOST J D, et al. Realization of a programmable two-qubit quantum processor[J]. Nat. Phys., 2010, 6(1): 13-16.
[98] HOWARD M, TWAMLEY J, WITTMANN C, et al. Quantum process tomography and Linblad estimation of a solid-state qubit[J]. New J. Phys., 2006, 8(3): 33.
[99] SHOR P W. Scheme for reducing decoherence in quantum computer memory[J]. Phys. Rev. A,1995, 52(4): R2493-R2496.
[100] CALDERBANK A R, SHOR P W. Good quantum error-correcting codes exist[J]. Phys. Rev.A, 1996, 54(2): 1098-1105.
[101] Multiple-particle interference and quantum error correction[J]. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1996, 452(1954):2551-2577.
[102] GOTTESMAN D. Class of quantum error-correcting codes saturating the quantum Hamming bound[J]. Phys. Rev. A, 1996, 54(3): 1862-1868.
[103] CORY D G, PRICE M D, MAAS W, et al. Experimental Quantum Error Correction[J]. Phys.Rev. Lett., 1998, 81(10): 2152-2155.
[104] KNILL E, LAFLAMME R, MARTINEZ R, et al. Benchmarking Quantum Computers: The Five-Qubit Error Correcting Code[J]. Phys. Rev. Lett., 2001, 86(25): 5811-5814.
[105] LU C Y, GAO W B, ZHANG J, et al. Experimental quantum coding against qubit loss error[J].Proceedings of the National Academy of Sciences, 2008, 105(32): 11050-11054