连续变量量子计算和量子纠错研究进展

王美红; 郝树宏; 秦忠忠; 苏晓龙

doi:10.7498/aps.71.20220635

摘要

量子计算机在解决某些复杂问题方面具有经典计算机无法比拟的优势. 实现大规模量子计算需建立具有通用性、可扩展性和容错性的硬件平台. 连续变量光学系统具有独特的优势, 是实现大规模量子计算的一种可行途径, 近年来受到了广泛关注. 基于测量的连续变量量子计算通过对大规模高斯簇态(cluster态)的测量和测量结果的前馈来实现计算, 为实现量子计算提供了一条可行的途径. 量子纠错是量子计算和量子通信中保护量子信息的重要环节. 本文简要介绍了基于cluster态的单向量子计算、基于光学薛定谔猫态的量子计算和连续变量量子纠错的基本原理和研究进展, 并讨论了连续变量量子计算面临的问题和挑战.

关键词:

Abstract

Quantum computation presents incomparable advantages over classical computer in solving some complex problems. To realize large-scale quantum computation, it is required to establish a hardware platform that is universal, scalable and fault tolerant. Continuous-variable optical system, which has unique advantages, is a feasible way to realize large-scale quantum computation and has attracted much attention in recent years. Measurement-based continuous-variable quantum computation realizes the computation by performing the measurement and feedforward of measurement results in large-scale Gaussian cluster states, and it provides an efficient method to realize quantum computation. Quantum error correction is an important part in quantum computation and quantum communication to protect quantum information. This review briefly introduces the basic principles and research advances in one-way quantum computation based on cluster states, quantum computation based on optical Schrödinger cat states and quantum error correction with continuous variables, and discusses the problems and challenges that the continuous-variable quantum computation is facing.

Keywords:

作者及机构信息

1.
山西大学光电研究所, 量子光学与光量子器件国家重点实验室, 极端光学协同创新中心, 太原　030006

2.
安徽工业大学数理科学与工程学院, 马鞍山　243000

通信作者: 苏晓龙, suxl@sxu.edu.cn

基金项目: 国家自然科学基金(批准号: 11834010, 62005149, 11804001, 11974227)、山西省“1331 工程”重点学科建设经费和山西省基础研究计划(批准号: 20210302121002, 20210302122002, 201901D211164)资助的课题

Authors and contacts

1.
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

2.
School of Mathematics and Physics, Anhui University of Technology, Maanshan 243000, China

Corresponding author: Su Xiao-Long, suxl@sxu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11834010, 62005149, 11804001, 11974227), the Fund for Shanxi “1331 Project” Key Subjects Construction, China, and the Fundamental Research Program of Shanxi Province, China (Grant Nos. 20210302121002, 20210302122002, 201901D211164).

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参考文献

[1]	Shor P W 1994 Proceedings 35th Annual Symposium on Foundations of Computer Science Santa Fe, American, November 20–22, 1994
[2]	Feynman R P 1982 Int. J. Theor. Phys. 21 467 Google Scholar
[3]	Lloyd S 1993 Science 261 1569 Google Scholar
[4]	Lloyd S 1994 Science 263 695 Google Scholar
[5]	Rarity J G, Ownes P C M, Tapster P R 1994 J. Mod. Opt. 41 2435 Google Scholar
[6]	Devoret M H, Schoelkopf R J 2013 Science 339 1169 Google Scholar
[7]	Gambetta J M, Chow J M, Steffen M 2017 NPJ Quantum Inf. 3 2 Google Scholar
[8]	Li Z Y, Yu H F, Tan X S, Zhao S P, Yu Y 2019 Chin. Phys. B 28 098505 Google Scholar
[9]	Gong M, Wang S, Zha C, et al. 2021 Science 372 948 Google Scholar
[10]	Huang H L, Wu D, Fan D, Zhu X 2020 Sci. Chin. Inf. Sci. 63 180501 Google Scholar
[11]	Pagano G, Bapat A, Becker P, Collins K S, De A, Hess P W, Kaplan H B, Kyprianidis A, Tan W L, Baldwin C, Brady L T, Deshpande A, Liu F, Jordan S, Gorshkov A V, Monroe C 2020 Proc. Natl. Acad. Sci. 117 25396 Google Scholar
[12]	Pino J M, Dreiling J M, Figgatt C, et al. 2021 Nature 592 209 Google Scholar
[13]	Watson T F, Philips S G J, Kawakami E, et al. 2018 Nature 555 633 Google Scholar
[14]	Hendrickx N W, Lawrie W I L, Russ M, et al. 2021 Nature 591 580 Google Scholar
[15]	Arrazola J M, Bergholm V, Brádler K, et al. 2021 Nature 591 54 Google Scholar
[16]	Zwanenburg F A, Dzurak A S, Morello A, Simmons M Y, Hollenberg L C L, Klimeck G, Rogge S, Coppersmith S N, Eriksson M A 2013 Rev. Mod. Phys. 85 961 Google Scholar
[17]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[18]	Yan Z, Zhang Y R, Gong M, et al. 2019 Science 364 753 Google Scholar
[19]	Wu Y, Bao W S, Cao S, et al. 2021 Phys. Rev. Lett. 127 180501 Google Scholar
[20]	Zhong H S, Wang H, Deng Y H, et al. 2020 Science 370 1460 Google Scholar
[21]	Zhong H S, Deng Y H, Qin J, et al. 2021 Phys. Rev. Lett. 127 180502 Google Scholar
[22]	van Loock P 2011 Laser Photonics Rev. 5 167 Google Scholar
[23]	Andersen U L, Neergaard-Nielsen J S, van Loock P, Furusawa A 2015 Nat. Phys. 11 713 Google Scholar
[24]	Braunstein S L, van Loock P 2005 Rev. Mod. Phys. 77 513 Google Scholar
[25]	Weedbrook C, Pirandola S, García-Patrón R, Cerf N J, Ralph T C, Shapiro J H, Lloyd S 2012 Rev. Mod. Phys. 84 621 Google Scholar
[26]	Huh J, Guerreschi G G, Peropadre B, McClean J R, Aspuru-Guzik A 2015 Nat. Photonics 9 615 Google Scholar
[27]	Hamilton C S, Kruse R, Sansoni L, Barkhofen S, Silberhorn C, Jex I 2017 Phys. Rev. Lett. 119 170501 Google Scholar
[28]	Arrazola J M, Bromley T R 2018 Phys. Rev. Lett. 121 030503 Google Scholar
[29]	Banchi L, Fingerhuth M, Babej T, Ing C, Arrazola J M 2020 Sci. Adv. 6 eaax1950 Google Scholar
[30]	Lau H K, Pooser R, Siopsis G, Weedbrook C 2017 Phys. Rev. Lett. 118 080501 Google Scholar
[31]	Schuld M, Killoran N 2019 Phys. Rev. Lett. 122 040504 Google Scholar
[32]	Killoran N, Bromley T R, Arrazola J M, Schuld M, Quesada N, Lloyd S 2019 Phys. Rev. Res. 1 033063 Google Scholar
[33]	Kalajdzievski T, Weedbrook C, Rebentrost P 2018 Phys. Rev. A 97 062311 Google Scholar
[34]	Arrazola J M, Kalajdzievski T, Weedbrook C, Lloyd S 2019 Phys. Rev. A 100 032306 Google Scholar
[35]	Adesso G, Illuminati F 2007 J. Phys. A:Math. Theor. 40 7821 Google Scholar
[36]	苏晓龙, 贾晓军, 彭堃墀 2016 物理学进展 36 101 Su X L, Jia X J, Peng K C 2016 Process phys. 36 101 (in Chinese)
[37]	Fukui K, Takeda S 2022 J. Phys. B:At. Mol. Opt. Phys. 55 012001 Google Scholar
[38]	Gu M, Weedbrook C, Menicucci N C, Ralph T C, van Loock P 2009 Phys. Rev. A 79 062318 Google Scholar
[39]	Furusawa A, van Loock P 2011 Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing (Hoboken: Wiley) p16
[40]	Lloyd S, Braunstein S L 1999 Phys. Rev. Lett. 82 1784 Google Scholar
[41]	Furusawa A, van Loock P 2011 Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing (Hoboken: Wiley) p58
[42]	Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188 Google Scholar
[43]	Menicucci N C, van Loock P, Gu M, Weedbrook C, Ralph T C, Nielsen M A 2006 Phys. Rev. Lett. 97 110501 Google Scholar
[44]	Zhang J, Braunstein S L 2006 Phys. Rev. A 73 032318 Google Scholar
[45]	Hao S, Deng X, Liu Y, Su X, Xie C, Peng K 2021 Chin. Phys. B 30 060312 Google Scholar
[46]	苏晓龙, 贾晓军, 谢常德, 彭堃墀 2010 物理 39 746 Su X L, Jia X J, Xie C D, Peng K C 2010 Physics 39 746
[47]	彭堃墀, 苏晓龙, 贾晓军, 谢常德 2012 山西大学学报 35 231 Google Scholar Peng K C, Su X L, Jia X J, Xie C D 2012 J. Shanxi Univ. 35 231 Google Scholar
[48]	Wang Y, Tian C, Su Q, Wang M, Su X 2019 Sci. Chin. Inf. Sci. 62 72501 Google Scholar
[49]	Su X, Wang M, Yan Z, Jia X, Xie C, Peng K 2020 Sci. Chin. Inf. Sci. 63 180503 Google Scholar
[50]	Menicucci N C, Flammia S T, van Loock P 2011 Phys. Rev. A 83 042335 Google Scholar
[51]	Su X, Tan A, Jia X, Zhang J, Xie C, Peng K 2007 Phys. Rev. Lett. 98 070502 Google Scholar
[52]	Yukawa M, Ukai R, van Loock P, Furusawa A 2008 Phys. Rev. A 78 012301 Google Scholar
[53]	Tan A, Wang Y, Jin X, Su X, Jia X, Zhang J, Xie C, Peng K 2008 Phys. Rev. A 78 013828 Google Scholar
[54]	Su X, Zhao Y, Hao S, Jia X, Xie C, Peng K 2012 Opt. Lett. 37 5178 Google Scholar
[55]	Pysher M, Miwa Y, Shahrokhshahi R, Bloomer R, Pfister O 2011 Phys. Rev. Lett. 107 030505 Google Scholar
[56]	Chen M, Menicucci N C, Pfister O 2014 Phys. Rev. Lett. 112 120505 Google Scholar
[57]	Roslund J, de Araújo R M, Jiang S, Fabre C, Treps N 2014 Nat. Photonics. 8 109 Google Scholar
[58]	Cai Y, Roslund J, Ferrini G, Arzani F, Xu X, Fabre C, Treps N 2017 Nat. Commun. 8 15645 Google Scholar
[59]	Menicucci N C 2011 Phys. Rev. A 83 062314 Google Scholar
[60]	Yokoyama S, Ukai R, Armstrong S C, Sornphiphatphong C, Kaji T, Suzuki S, Yoshikawa J I, Yonezawa H, Menicucci N C, Furusawa A 2013 Nat. Photonics 7 982 Google Scholar
[61]	Yoshikawa J I, Yokoyama S, Kaji T, Sornphiphatphong C, Shiozawa Y, Makino K, Furusawa A 2016 APL Photonics 1 060801 Google Scholar
[62]	Larsen M V, Guo X, Breum C R, Neergaard-Nielsen J S, Andersen U L 2019 Science 366 369 Google Scholar
[63]	Asavanant W, Shiozawa Y, Yokoyama S, et al. 2019 Science 366 373 Google Scholar
[64]	Raussendorf R, Harrington J 2007 Phys. Rev. Lett. 98 190504 Google Scholar
[65]	Raussendorf R, Harrington J, Goyal K 2007 New J. Phys. 9 199 Google Scholar
[66]	Fukui K, Asavanant W, Furusawa A 2020 Phys. Rev. A 102 032614 Google Scholar
[67]	Yoshikawa J I, Hayashi T, Akiyama T, Takei N, Huck A, Andersen U L, Furusawa A 2007 Phys. Rev. A 76 060301 Google Scholar
[68]	Yoshikawa J I, Miwa Y, Huck A, Andersen U L, van Loock P, Furusawa A 2008 Phys. Rev. Lett. 101 250501 Google Scholar
[69]	Miwa Y, Yoshikawa J I, van Loock P, Furusawa A 2009 Phys. Rev. A 80 050303 Google Scholar
[70]	Ukai R, Yokoyama S, Yoshikawa J I, van Loock P, Furusawa A 2011 Phys. Rev. Lett. 107 250501 Google Scholar
[71]	Ukai R, Iwata N, Shimokawa Y, Armstrong S C, Politi A, Yoshikawa J I, van Loock P, Furusawa A 2011 Phys. Rev. Lett. 106 240504 Google Scholar
[72]	Wang Y, Su X, Shen H, Tan A, Xie C, Peng K 2010 Phys. Rev. A 81 022311 Google Scholar
[73]	Hao S, Deng X, Su X, Jia X, Xie C, Peng K 2014 Phys. Rev. A 89 032311 Google Scholar
[74]	Su X, Hao S, Deng X, Ma L, Wang M, Jia X, Xie C, Peng K 2013 Nat. Commun. 4 2828 Google Scholar
[75]	Asavanant W, Charoensombutamon B, Yokoyama S, et al. 2021 Phys. Rev. Appl. 16 034005 Google Scholar
[76]	Larsen M V, Guo X, Breum C R, Neergaard-Nielsen J S, Andersen U L 2021 Nat. Phys. 17 1018 Google Scholar
[77]	Gottesman D, Kitaev A, Preskill J 2001 Phys. Rev. A 64 012310 Google Scholar
[78]	Miyata K, Ogawa H, Marek P, Filip R, Yonezawa H, Yoshikawa J I, Furusawa A 2016 Phys. Rev. A 93 022301 Google Scholar
[79]	Sabapathy K K, Weedbrook C 2018 Phys. Rev. A 97 062315 Google Scholar
[80]	Yukawa M, Miyata K, Yonezawa H, Marek P, Filip R, Furusawa A 2013 Phys. Rev. A 88 053816 Google Scholar
[81]	Masada G, Miyata K, Politi A, Hashimoto T, O’Brien J L, Furusawa A 2015 Nat. Photonics 9 316 Google Scholar
[82]	Yang Z, Jahanbozorgi M, Jeong D, Sun S, Pfister O, Lee H, Yi X 2021 Nat. Commun. 12 4781 Google Scholar
[83]	Dutt A, Luke K, Manipatruni S, Gaeta A L, Nussenzveig P, Lipson M 2015 Phys. Rev. Appl. 3 044005 Google Scholar
[84]	Zhao Y, Okawachi Y, Jang J K, Ji X, Lipson M, Gaeta A L 2020 Phys. Rev. Lett. 124 193601 Google Scholar
[85]	Vaidya V D, Morrison B, Helt L G, et al. 2020 Sci. Adv. 6 eaba9186 Google Scholar
[86]	Zhang Q Y, Xu P, Zhu S N 2018 Chin. Phys. B 27 054207 Google Scholar
[87]	Kaiser F, Fedrici B, Zavatta A, D’Auria V, Tanzilli S 2016 Optica 3 362 Google Scholar
[88]	Fürst J U, Strekalov D V, Elser D, Aiello A, Andersen U L, Marquardt Ch, Leuchs G 2011 Phys. Rev. Lett. 106 113901 Google Scholar
[89]	Lenzini F, Janousek J, Thearle O, Villa M, Haylock B, Kasture S, Cui L, Phan H P, Dao D V, Yonezawa H, Lam P K, Huntington E H, Lobino M 2018 Sci. Adv. 4 eaat9331 Google Scholar
[90]	Qi Y, Li Y 2020 Nanophotonics 9 1287 Google Scholar
[91]	Chen P K, Briggs I, Hou S, Fan L 2022 Opt. Lett. 47 1506 Google Scholar
[92]	Schrödinger E 1935 Naturwissenschaften 23 807 Google Scholar
[93]	Haroche S 2013 Rev. Mod. Phys. 85 1083 Google Scholar
[94]	Arndt M, Hornberger K 2014 Nat. Phys. 10 271 Google Scholar
[95]	Ralph T C, Gilchrist A, Milburn G J, Munro W J, Glancy S 2003 Phys. Rev. A 68 042319 Google Scholar
[96]	Jeong H, Kim M S 2002 Phys. Rev. A 65 042305 Google Scholar
[97]	Lund A P, Ralph T C, Haselgrove H L 2008 Phys. Rev. Lett. 100 030503 Google Scholar
[98]	Sychev D V, Ulanov A E, Tiunov E S, Pushkina A A, Kuzhamuratov A, Novikov V, Lvovsky A I 2018 Nat. Commun. 9 3672 Google Scholar
[99]	Dakna M, Anhut T, Opatrnýn T, Knöll L, Welsch D G 1997 Phys. Rev. A 55 3184 Google Scholar
[100]	Ourjoumtsev A, Tualle-Brouri R, Laurat J, Grangier P 2006 Science 312 83 Google Scholar
[101]	Neergaard-Nielsen J S, Melholt Nielsen B, Hettich C, Mølmer K, Polzik E S 2006 Phys. Rev. Lett. 97 083604 Google Scholar
[102]	Wakui K, Takahashi H, Furusawa A, Sasaki M 2007 Opt. Express 15 3568 Google Scholar
[103]	Lee N, Benichi H, Takeno Y, Takeda S, Webb J, Huntington E, Furusawa A 2011 Science 332 330 Google Scholar
[104]	Marek P, Fiurášek J 2010 Phys. Rev. A 82 014304 Google Scholar
[105]	Tipsmark A, Dong R, Laghaout A, Marek P, Ježek M, Andersen U L 2011 Phys. Rev. A 84 050301 Google Scholar
[106]	Blandino R, Ferreyrol F, Barbieri M, Grangier P, Tualle-Brouri R 2012 New J. Phys. 14 013017 Google Scholar
[107]	Ourjoumtsev A, Ferreyrol F, Tualle-Brouri R, Grangier P 2009 Nat. Phys. 5 189 Google Scholar
[108]	Sychev D V, Novikov V A, Pirov K K, Simon C, Lvovsky A I 2019 Optica 6 1425 Google Scholar
[109]	Braunstein S L 1998 Nature 394 47 Google Scholar
[110]	Lloyd S, Slotine J J E 1998 Phys. Rev. Lett. 80 4088 Google Scholar
[111]	Braunstein S L 1998 Phys. Rev. Lett. 80 4084 Google Scholar
[112]	Walker T A, Braunstein S L 2010 Phys. Rev. A 81 062305 Google Scholar
[113]	Wilde M M, Krovi H, Brun T A 2007 Phys. Rev. A 76 052308 Google Scholar
[114]	Niset J, Andersen U L, Cerf N J 2008 Phys. Rev. Lett. 101 130503 Google Scholar
[115]	Niset J, Fiurášek J, Cerf N J 2009 Phys. Rev. Lett. 102 120501 Google Scholar
[116]	Aoki T, Takahashi G, Kajiya T, Yoshikawa J I, Braunstein S L, van Loock P, Furusawa A 2009 Nat. Phys. 5 541 Google Scholar
[117]	Lassen M, Berni A, Madsen L S, Filip R, Andersen U L 2013 Phys. Rev. Lett. 111 180502 Google Scholar
[118]	Hao S, Su X, Tian C, Xie C, Peng K 2015 Sci. Rep. 5 15462 Google Scholar
[119]	Ralph T C 2011 Phys. Rev. A 84 022339 Google Scholar
[120]	Glancy S, Knill E 2006 Phys. Rev. A 73 012325 Google Scholar
[121]	Albert V V, Noh K, Duivenvoorden K, Young D J, Brierley R T, Reinhold P, Vuillot C, Li L, Shen C, Girvin S M, Terhal B M, Jiang L 2018 Phys. Rev. A 97 032346 Google Scholar
[122]	Flühmann C, Nguyen T L, Marinelli M, Negnevitsky V, Mehta K, Home J P 2019 Nature 566 513 Google Scholar
[123]	Campagne-Ibarcq P, Eickbusch A, Touzard S, Zalys-Geller E, Frattini N E, Sivak V V, Reinhold P, Puri S, Shankar S, Schoelkopf R J, Frunzio L, Mirrahimi M, Devoret M H 2020 Nature 584 368 Google Scholar
[124]	Vasconcelos H M, Sanz L, Glancy S 2010 Opt. Lett. 35 3261 Google Scholar
[125]	Fukui K, Takeda S, Endo M, Asavanant W, Yoshikawa J I, van Loock P, Furusawa A 2022 Phys. Rev. Lett. 128 240503 Google Scholar
[126]	Su D, Myers C R, Sabapathy K K 2019 Phys. Rev. A 100 052301 Google Scholar
[127]	Fowler A G, Goyal K 2009 Quantum Inf. Comput. 9 727 Google Scholar
[128]	Raussendorf R, Harrington J, Goyal K 2006 Ann. Phys. 321 2242 Google Scholar
[129]	Stern A, Lindner N H 2013 Science 339 1179 Google Scholar
[130]	Zhang J, Xie C, Peng K, van Loock P 2008 Phys. Rev. A 78 052121 Google Scholar
[131]	Morimae T 2013 Phys. Rev. A 88 042311 Google Scholar
[132]	Menicucci N C, Baragiola B Q, Demarie T F, Brennen G K 2018 Phys. Rev. A 97 032345 Google Scholar
[133]	Milne D F, Korolkova N V, van Loock P 2012 Phys. Rev. A 85 052325 Google Scholar
[134]	Menicucci N C 2014 Phys. Rev. Lett. 112 120504 Google Scholar
[135]	Hao S, Wang M, Wang D, Su X 2021 Phys. Rev. A 103 052407 Google Scholar

施引文献

图 1 平衡零拍探测系统示意图^[36]

Fig. 1. Schematic of balance homodyne detection^[36] .

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图 2 平移算符对量子态的作用效果^[39]

Fig. 2. Effect of displacement operation on quantum state^[39]

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图 3 多组份cluster态示意图 (a) 四组份线性cluster态^[45]; (b) 二维cluster态^[45]; (c) 三维cluster态^[45]

Fig. 3. Schematic of multipartite cluster entangled states: (a) Linear four-mode cluster state^[45]; (b) two-dimensional cluster state^[45]; (c) three-dimensional cluster state^[45].

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图 4 立方位相门 (a)基于立方位相态实现立方位相门的线路图^[77]; (b)立方位相态的产生方案^[37]

Fig. 4. Cubic phase gate: (a) The cubic phase gate by the measurement-induced scheme using the cubic phase state^[77]; (b) the preparation of the cubic phase state^[37].

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图 5 基于光学猫态的Hadamard门方案示意图^[104]

Fig. 5. Schematic of Hadamard gate based on optical cat state^[104].

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图 6 基于光学猫态的位相旋转门方案示意图^[95]

Fig. 6. Schematic of phase rotation gate based on optical cat state^[95].

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图 7 基于光学猫态的可控位相门方案示意图^[95]

Fig. 7. Schematic of controlled phase gate based on optical cat state^[95].

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图 8 基于五波包部分编码方式的连续变量量子纠错方案^[118]

Fig. 8. Scheme of CV quantum error correction with five-wave-packet code^[118].

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图 9 GKP量子比特的编码方式^[77]

Fig. 9. The codeword for the GKP qubit^[77].

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图 10 基于cluster态的连续变量拓扑误差修正方案 (a) 八组份拓扑结构连续变量cluster 纠缠态的图态表示^[135]; (b) 产生八组份连续变量cluster 纠缠态的分束器网络^[135]

Fig. 10. Scheme of topological error correction with CV a Gaussian cluster state: (a) The graph structure of the topological eight-partite CV cluster state; (b) the beam-splitter network for the preparation of the cluster state^[135].

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表 1 离散变量和连续变量量子逻辑门的比较^[37]

Table 1. Comparison between quantum logical gates with describe variables and continuous variables^[37].

	离散变量 (qubits)	连续变量 (qumodes)
计算基矢	$ \{{ \|0 \rangle }_{\mathrm{L}}, { \|1 \rangle }_{\mathrm{L}} \} $	$ \{{{ \|s \rangle }_{x}\}}_{\mathrm{s}\in \mathbb{R}} $
共轭基矢	$ \big\{{{ \|\pm \rangle }_{\mathrm{L}}=( \|0 \rangle }_{\mathrm{L}}\pm { \|1 \rangle }_{\mathrm{L}})/\sqrt{2} \big \} $	${ \bigg\{ { \|t \rangle }_{p}=\dfrac{1}{\sqrt{2\mathrm{\pi } } } \displaystyle\int_{-\infty }^{\infty }\mathrm{d}s{\mathrm{e} }^{\mathrm{i}st}{ \|s \rangle }_{x} \bigg\} }_{t\in \mathbb{R} }$
编码	$ { \|\psi \rangle =\alpha \|0 \rangle }_{\mathrm{L}}+\beta { \|1 \rangle }_{\mathrm{L}} $$ ({ \|\alpha \|}^{2}+{ \|\beta \|}^{2}=1 $)	$\|\psi \rangle = \displaystyle\int_{-\infty }^{\infty }\mathrm{d}s\psi (s ){ \|s \rangle }_{x} \bigg(\displaystyle\int_{-\infty }^{\infty }\mathrm{d}s{ \|\psi (s ) \|}^{2}=1 \bigg)$
探测方式	光子探测	平衡零拍探测
量子逻辑门	Bit-flip: $ {\widehat{X} \|0 \rangle }_{\mathrm{L}}={ \|1 \rangle }_{\mathrm{L}}, {\widehat{X} \|1 \rangle }_{\mathrm{L}}={ \|0 \rangle }_{\mathrm{L}} $	x方向平移: $ \widehat{X} (v ){ \|s \rangle }_{x}={ \|s+v \rangle }_{x} $
	Phase-flip: $ {\widehat{Z} \|0 \rangle }_{\mathrm{L}}={ \|0 \rangle }_{\mathrm{L}}, {\widehat{Z} \|1 \rangle }_{\mathrm{L}}={- \|1 \rangle }_{\mathrm{L}} $	p方向平移: $ \widehat{Z} (u ){ \|t \rangle }_{p}={ \|t+u \rangle }_{p} $
	Hadamard门:$ {\widehat{H} \|0 \rangle }_{\mathrm{L}}={ \|+ \rangle }_{\mathrm{L}}, {\widehat{H} \|1 \rangle }_{\mathrm{L}}={ \|- \rangle }_{\mathrm{L}} $	傅立叶变换: $\widehat{R} ( {\mathrm{\pi } }/{2} ){ \|s \rangle }_{x}={ \|s \rangle }_{p}, \widehat{R} ( {\mathrm{\pi } }/{2} ){ \|t \rangle }_{p}={ \|-t \rangle }_{x}$
	可控非门: $ {\widehat{CX} \|0 \rangle }_{\mathrm{L}}{ \|0 (1 ) \rangle }_{\mathrm{L}}={ \|0 \rangle }_{\mathrm{L}}{ \|0 (1 ) \rangle }_{\mathrm{L}} $	可控X门: $ {\widehat{CX} \|{s}_{1} \rangle }_{{q}_{1}}{ \|{s}_{2} \rangle }_{{q}_{2}}={ \|{s}_{1} \rangle }_{{q}_{1}}{ \|{s}_{2}+{s}_{1} \rangle }_{{q}_{2}} $
	$ {\widehat{CX} \|1 \rangle }_{\mathrm{L}}{ \|0 (1 ) \rangle }_{\mathrm{L}}={ \|1 \rangle }_{\mathrm{L}}{ \|1 (0 ) \rangle }_{\mathrm{L}} $	$ {\widehat{CX} \|{t}_{1} \rangle }_{{p}_{1}}{ \|{t}_{2} \rangle }_{{p}_{2}}={ \|{t}_{1}-{t}_{2} \rangle }_{{p}_{1}}{ \|{t}_{2} \rangle }_{{p}_{2}} $

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[1]	Shor P W 1994 Proceedings 35th Annual Symposium on Foundations of Computer Science Santa Fe, American, November 20–22, 1994
[2]	Feynman R P 1982 Int. J. Theor. Phys. 21 467 Google Scholar
[3]	Lloyd S 1993 Science 261 1569 Google Scholar
[4]	Lloyd S 1994 Science 263 695 Google Scholar
[5]	Rarity J G, Ownes P C M, Tapster P R 1994 J. Mod. Opt. 41 2435 Google Scholar
[6]	Devoret M H, Schoelkopf R J 2013 Science 339 1169 Google Scholar
[7]	Gambetta J M, Chow J M, Steffen M 2017 NPJ Quantum Inf. 3 2 Google Scholar
[8]	Li Z Y, Yu H F, Tan X S, Zhao S P, Yu Y 2019 Chin. Phys. B 28 098505 Google Scholar
[9]	Gong M, Wang S, Zha C, et al. 2021 Science 372 948 Google Scholar
[10]	Huang H L, Wu D, Fan D, Zhu X 2020 Sci. Chin. Inf. Sci. 63 180501 Google Scholar
[11]	Pagano G, Bapat A, Becker P, Collins K S, De A, Hess P W, Kaplan H B, Kyprianidis A, Tan W L, Baldwin C, Brady L T, Deshpande A, Liu F, Jordan S, Gorshkov A V, Monroe C 2020 Proc. Natl. Acad. Sci. 117 25396 Google Scholar
[12]	Pino J M, Dreiling J M, Figgatt C, et al. 2021 Nature 592 209 Google Scholar
[13]	Watson T F, Philips S G J, Kawakami E, et al. 2018 Nature 555 633 Google Scholar
[14]	Hendrickx N W, Lawrie W I L, Russ M, et al. 2021 Nature 591 580 Google Scholar
[15]	Arrazola J M, Bergholm V, Brádler K, et al. 2021 Nature 591 54 Google Scholar
[16]	Zwanenburg F A, Dzurak A S, Morello A, Simmons M Y, Hollenberg L C L, Klimeck G, Rogge S, Coppersmith S N, Eriksson M A 2013 Rev. Mod. Phys. 85 961 Google Scholar
[17]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[18]	Yan Z, Zhang Y R, Gong M, et al. 2019 Science 364 753 Google Scholar
[19]	Wu Y, Bao W S, Cao S, et al. 2021 Phys. Rev. Lett. 127 180501 Google Scholar
[20]	Zhong H S, Wang H, Deng Y H, et al. 2020 Science 370 1460 Google Scholar
[21]	Zhong H S, Deng Y H, Qin J, et al. 2021 Phys. Rev. Lett. 127 180502 Google Scholar
[22]	van Loock P 2011 Laser Photonics Rev. 5 167 Google Scholar
[23]	Andersen U L, Neergaard-Nielsen J S, van Loock P, Furusawa A 2015 Nat. Phys. 11 713 Google Scholar
[24]	Braunstein S L, van Loock P 2005 Rev. Mod. Phys. 77 513 Google Scholar
[25]	Weedbrook C, Pirandola S, García-Patrón R, Cerf N J, Ralph T C, Shapiro J H, Lloyd S 2012 Rev. Mod. Phys. 84 621 Google Scholar
[26]	Huh J, Guerreschi G G, Peropadre B, McClean J R, Aspuru-Guzik A 2015 Nat. Photonics 9 615 Google Scholar
[27]	Hamilton C S, Kruse R, Sansoni L, Barkhofen S, Silberhorn C, Jex I 2017 Phys. Rev. Lett. 119 170501 Google Scholar
[28]	Arrazola J M, Bromley T R 2018 Phys. Rev. Lett. 121 030503 Google Scholar
[29]	Banchi L, Fingerhuth M, Babej T, Ing C, Arrazola J M 2020 Sci. Adv. 6 eaax1950 Google Scholar
[30]	Lau H K, Pooser R, Siopsis G, Weedbrook C 2017 Phys. Rev. Lett. 118 080501 Google Scholar
[31]	Schuld M, Killoran N 2019 Phys. Rev. Lett. 122 040504 Google Scholar
[32]	Killoran N, Bromley T R, Arrazola J M, Schuld M, Quesada N, Lloyd S 2019 Phys. Rev. Res. 1 033063 Google Scholar
[33]	Kalajdzievski T, Weedbrook C, Rebentrost P 2018 Phys. Rev. A 97 062311 Google Scholar
[34]	Arrazola J M, Kalajdzievski T, Weedbrook C, Lloyd S 2019 Phys. Rev. A 100 032306 Google Scholar
[35]	Adesso G, Illuminati F 2007 J. Phys. A:Math. Theor. 40 7821 Google Scholar
[36]	苏晓龙, 贾晓军, 彭堃墀 2016 物理学进展 36 101 Su X L, Jia X J, Peng K C 2016 Process phys. 36 101 (in Chinese)
[37]	Fukui K, Takeda S 2022 J. Phys. B:At. Mol. Opt. Phys. 55 012001 Google Scholar
[38]	Gu M, Weedbrook C, Menicucci N C, Ralph T C, van Loock P 2009 Phys. Rev. A 79 062318 Google Scholar
[39]	Furusawa A, van Loock P 2011 Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing (Hoboken: Wiley) p16
[40]	Lloyd S, Braunstein S L 1999 Phys. Rev. Lett. 82 1784 Google Scholar
[41]	Furusawa A, van Loock P 2011 Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing (Hoboken: Wiley) p58
[42]	Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188 Google Scholar
[43]	Menicucci N C, van Loock P, Gu M, Weedbrook C, Ralph T C, Nielsen M A 2006 Phys. Rev. Lett. 97 110501 Google Scholar
[44]	Zhang J, Braunstein S L 2006 Phys. Rev. A 73 032318 Google Scholar
[45]	Hao S, Deng X, Liu Y, Su X, Xie C, Peng K 2021 Chin. Phys. B 30 060312 Google Scholar
[46]	苏晓龙, 贾晓军, 谢常德, 彭堃墀 2010 物理 39 746 Su X L, Jia X J, Xie C D, Peng K C 2010 Physics 39 746
[47]	彭堃墀, 苏晓龙, 贾晓军, 谢常德 2012 山西大学学报 35 231 Google Scholar Peng K C, Su X L, Jia X J, Xie C D 2012 J. Shanxi Univ. 35 231 Google Scholar
[48]	Wang Y, Tian C, Su Q, Wang M, Su X 2019 Sci. Chin. Inf. Sci. 62 72501 Google Scholar
[49]	Su X, Wang M, Yan Z, Jia X, Xie C, Peng K 2020 Sci. Chin. Inf. Sci. 63 180503 Google Scholar
[50]	Menicucci N C, Flammia S T, van Loock P 2011 Phys. Rev. A 83 042335 Google Scholar
[51]	Su X, Tan A, Jia X, Zhang J, Xie C, Peng K 2007 Phys. Rev. Lett. 98 070502 Google Scholar
[52]	Yukawa M, Ukai R, van Loock P, Furusawa A 2008 Phys. Rev. A 78 012301 Google Scholar
[53]	Tan A, Wang Y, Jin X, Su X, Jia X, Zhang J, Xie C, Peng K 2008 Phys. Rev. A 78 013828 Google Scholar
[54]	Su X, Zhao Y, Hao S, Jia X, Xie C, Peng K 2012 Opt. Lett. 37 5178 Google Scholar
[55]	Pysher M, Miwa Y, Shahrokhshahi R, Bloomer R, Pfister O 2011 Phys. Rev. Lett. 107 030505 Google Scholar
[56]	Chen M, Menicucci N C, Pfister O 2014 Phys. Rev. Lett. 112 120505 Google Scholar
[57]	Roslund J, de Araújo R M, Jiang S, Fabre C, Treps N 2014 Nat. Photonics. 8 109 Google Scholar
[58]	Cai Y, Roslund J, Ferrini G, Arzani F, Xu X, Fabre C, Treps N 2017 Nat. Commun. 8 15645 Google Scholar
[59]	Menicucci N C 2011 Phys. Rev. A 83 062314 Google Scholar
[60]	Yokoyama S, Ukai R, Armstrong S C, Sornphiphatphong C, Kaji T, Suzuki S, Yoshikawa J I, Yonezawa H, Menicucci N C, Furusawa A 2013 Nat. Photonics 7 982 Google Scholar
[61]	Yoshikawa J I, Yokoyama S, Kaji T, Sornphiphatphong C, Shiozawa Y, Makino K, Furusawa A 2016 APL Photonics 1 060801 Google Scholar
[62]	Larsen M V, Guo X, Breum C R, Neergaard-Nielsen J S, Andersen U L 2019 Science 366 369 Google Scholar
[63]	Asavanant W, Shiozawa Y, Yokoyama S, et al. 2019 Science 366 373 Google Scholar
[64]	Raussendorf R, Harrington J 2007 Phys. Rev. Lett. 98 190504 Google Scholar
[65]	Raussendorf R, Harrington J, Goyal K 2007 New J. Phys. 9 199 Google Scholar
[66]	Fukui K, Asavanant W, Furusawa A 2020 Phys. Rev. A 102 032614 Google Scholar
[67]	Yoshikawa J I, Hayashi T, Akiyama T, Takei N, Huck A, Andersen U L, Furusawa A 2007 Phys. Rev. A 76 060301 Google Scholar
[68]	Yoshikawa J I, Miwa Y, Huck A, Andersen U L, van Loock P, Furusawa A 2008 Phys. Rev. Lett. 101 250501 Google Scholar
[69]	Miwa Y, Yoshikawa J I, van Loock P, Furusawa A 2009 Phys. Rev. A 80 050303 Google Scholar
[70]	Ukai R, Yokoyama S, Yoshikawa J I, van Loock P, Furusawa A 2011 Phys. Rev. Lett. 107 250501 Google Scholar
[71]	Ukai R, Iwata N, Shimokawa Y, Armstrong S C, Politi A, Yoshikawa J I, van Loock P, Furusawa A 2011 Phys. Rev. Lett. 106 240504 Google Scholar
[72]	Wang Y, Su X, Shen H, Tan A, Xie C, Peng K 2010 Phys. Rev. A 81 022311 Google Scholar
[73]	Hao S, Deng X, Su X, Jia X, Xie C, Peng K 2014 Phys. Rev. A 89 032311 Google Scholar
[74]	Su X, Hao S, Deng X, Ma L, Wang M, Jia X, Xie C, Peng K 2013 Nat. Commun. 4 2828 Google Scholar
[75]	Asavanant W, Charoensombutamon B, Yokoyama S, et al. 2021 Phys. Rev. Appl. 16 034005 Google Scholar
[76]	Larsen M V, Guo X, Breum C R, Neergaard-Nielsen J S, Andersen U L 2021 Nat. Phys. 17 1018 Google Scholar
[77]	Gottesman D, Kitaev A, Preskill J 2001 Phys. Rev. A 64 012310 Google Scholar
[78]	Miyata K, Ogawa H, Marek P, Filip R, Yonezawa H, Yoshikawa J I, Furusawa A 2016 Phys. Rev. A 93 022301 Google Scholar
[79]	Sabapathy K K, Weedbrook C 2018 Phys. Rev. A 97 062315 Google Scholar
[80]	Yukawa M, Miyata K, Yonezawa H, Marek P, Filip R, Furusawa A 2013 Phys. Rev. A 88 053816 Google Scholar
[81]	Masada G, Miyata K, Politi A, Hashimoto T, O’Brien J L, Furusawa A 2015 Nat. Photonics 9 316 Google Scholar
[82]	Yang Z, Jahanbozorgi M, Jeong D, Sun S, Pfister O, Lee H, Yi X 2021 Nat. Commun. 12 4781 Google Scholar
[83]	Dutt A, Luke K, Manipatruni S, Gaeta A L, Nussenzveig P, Lipson M 2015 Phys. Rev. Appl. 3 044005 Google Scholar
[84]	Zhao Y, Okawachi Y, Jang J K, Ji X, Lipson M, Gaeta A L 2020 Phys. Rev. Lett. 124 193601 Google Scholar
[85]	Vaidya V D, Morrison B, Helt L G, et al. 2020 Sci. Adv. 6 eaba9186 Google Scholar
[86]	Zhang Q Y, Xu P, Zhu S N 2018 Chin. Phys. B 27 054207 Google Scholar
[87]	Kaiser F, Fedrici B, Zavatta A, D’Auria V, Tanzilli S 2016 Optica 3 362 Google Scholar
[88]	Fürst J U, Strekalov D V, Elser D, Aiello A, Andersen U L, Marquardt Ch, Leuchs G 2011 Phys. Rev. Lett. 106 113901 Google Scholar
[89]	Lenzini F, Janousek J, Thearle O, Villa M, Haylock B, Kasture S, Cui L, Phan H P, Dao D V, Yonezawa H, Lam P K, Huntington E H, Lobino M 2018 Sci. Adv. 4 eaat9331 Google Scholar
[90]	Qi Y, Li Y 2020 Nanophotonics 9 1287 Google Scholar
[91]	Chen P K, Briggs I, Hou S, Fan L 2022 Opt. Lett. 47 1506 Google Scholar
[92]	Schrödinger E 1935 Naturwissenschaften 23 807 Google Scholar
[93]	Haroche S 2013 Rev. Mod. Phys. 85 1083 Google Scholar
[94]	Arndt M, Hornberger K 2014 Nat. Phys. 10 271 Google Scholar
[95]	Ralph T C, Gilchrist A, Milburn G J, Munro W J, Glancy S 2003 Phys. Rev. A 68 042319 Google Scholar
[96]	Jeong H, Kim M S 2002 Phys. Rev. A 65 042305 Google Scholar
[97]	Lund A P, Ralph T C, Haselgrove H L 2008 Phys. Rev. Lett. 100 030503 Google Scholar
[98]	Sychev D V, Ulanov A E, Tiunov E S, Pushkina A A, Kuzhamuratov A, Novikov V, Lvovsky A I 2018 Nat. Commun. 9 3672 Google Scholar
[99]	Dakna M, Anhut T, Opatrnýn T, Knöll L, Welsch D G 1997 Phys. Rev. A 55 3184 Google Scholar
[100]	Ourjoumtsev A, Tualle-Brouri R, Laurat J, Grangier P 2006 Science 312 83 Google Scholar
[101]	Neergaard-Nielsen J S, Melholt Nielsen B, Hettich C, Mølmer K, Polzik E S 2006 Phys. Rev. Lett. 97 083604 Google Scholar
[102]	Wakui K, Takahashi H, Furusawa A, Sasaki M 2007 Opt. Express 15 3568 Google Scholar
[103]	Lee N, Benichi H, Takeno Y, Takeda S, Webb J, Huntington E, Furusawa A 2011 Science 332 330 Google Scholar
[104]	Marek P, Fiurášek J 2010 Phys. Rev. A 82 014304 Google Scholar
[105]	Tipsmark A, Dong R, Laghaout A, Marek P, Ježek M, Andersen U L 2011 Phys. Rev. A 84 050301 Google Scholar
[106]	Blandino R, Ferreyrol F, Barbieri M, Grangier P, Tualle-Brouri R 2012 New J. Phys. 14 013017 Google Scholar
[107]	Ourjoumtsev A, Ferreyrol F, Tualle-Brouri R, Grangier P 2009 Nat. Phys. 5 189 Google Scholar
[108]	Sychev D V, Novikov V A, Pirov K K, Simon C, Lvovsky A I 2019 Optica 6 1425 Google Scholar
[109]	Braunstein S L 1998 Nature 394 47 Google Scholar
[110]	Lloyd S, Slotine J J E 1998 Phys. Rev. Lett. 80 4088 Google Scholar
[111]	Braunstein S L 1998 Phys. Rev. Lett. 80 4084 Google Scholar
[112]	Walker T A, Braunstein S L 2010 Phys. Rev. A 81 062305 Google Scholar
[113]	Wilde M M, Krovi H, Brun T A 2007 Phys. Rev. A 76 052308 Google Scholar
[114]	Niset J, Andersen U L, Cerf N J 2008 Phys. Rev. Lett. 101 130503 Google Scholar
[115]	Niset J, Fiurášek J, Cerf N J 2009 Phys. Rev. Lett. 102 120501 Google Scholar
[116]	Aoki T, Takahashi G, Kajiya T, Yoshikawa J I, Braunstein S L, van Loock P, Furusawa A 2009 Nat. Phys. 5 541 Google Scholar
[117]	Lassen M, Berni A, Madsen L S, Filip R, Andersen U L 2013 Phys. Rev. Lett. 111 180502 Google Scholar
[118]	Hao S, Su X, Tian C, Xie C, Peng K 2015 Sci. Rep. 5 15462 Google Scholar
[119]	Ralph T C 2011 Phys. Rev. A 84 022339 Google Scholar
[120]	Glancy S, Knill E 2006 Phys. Rev. A 73 012325 Google Scholar
[121]	Albert V V, Noh K, Duivenvoorden K, Young D J, Brierley R T, Reinhold P, Vuillot C, Li L, Shen C, Girvin S M, Terhal B M, Jiang L 2018 Phys. Rev. A 97 032346 Google Scholar
[122]	Flühmann C, Nguyen T L, Marinelli M, Negnevitsky V, Mehta K, Home J P 2019 Nature 566 513 Google Scholar
[123]	Campagne-Ibarcq P, Eickbusch A, Touzard S, Zalys-Geller E, Frattini N E, Sivak V V, Reinhold P, Puri S, Shankar S, Schoelkopf R J, Frunzio L, Mirrahimi M, Devoret M H 2020 Nature 584 368 Google Scholar
[124]	Vasconcelos H M, Sanz L, Glancy S 2010 Opt. Lett. 35 3261 Google Scholar
[125]	Fukui K, Takeda S, Endo M, Asavanant W, Yoshikawa J I, van Loock P, Furusawa A 2022 Phys. Rev. Lett. 128 240503 Google Scholar
[126]	Su D, Myers C R, Sabapathy K K 2019 Phys. Rev. A 100 052301 Google Scholar
[127]	Fowler A G, Goyal K 2009 Quantum Inf. Comput. 9 727 Google Scholar
[128]	Raussendorf R, Harrington J, Goyal K 2006 Ann. Phys. 321 2242 Google Scholar
[129]	Stern A, Lindner N H 2013 Science 339 1179 Google Scholar
[130]	Zhang J, Xie C, Peng K, van Loock P 2008 Phys. Rev. A 78 052121 Google Scholar
[131]	Morimae T 2013 Phys. Rev. A 88 042311 Google Scholar
[132]	Menicucci N C, Baragiola B Q, Demarie T F, Brennen G K 2018 Phys. Rev. A 97 032345 Google Scholar
[133]	Milne D F, Korolkova N V, van Loock P 2012 Phys. Rev. A 85 052325 Google Scholar
[134]	Menicucci N C 2014 Phys. Rev. Lett. 112 120504 Google Scholar
[135]	Hao S, Wang M, Wang D, Su X 2021 Phys. Rev. A 103 052407 Google Scholar

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	离散变量 (qubits)	连续变量 (qumodes)
计算基矢	$ \{{ \|0 \rangle }_{\mathrm{L}}, { \|1 \rangle }_{\mathrm{L}} \} $	$ \{{{ \|s \rangle }_{x}\}}_{\mathrm{s}\in \mathbb{R}} $
共轭基矢	$ \big\{{{ \|\pm \rangle }_{\mathrm{L}}=( \|0 \rangle }_{\mathrm{L}}\pm { \|1 \rangle }_{\mathrm{L}})/\sqrt{2} \big \} $	${ \bigg\{ { \|t \rangle }_{p}=\dfrac{1}{\sqrt{2\mathrm{\pi } } } \displaystyle\int_{-\infty }^{\infty }\mathrm{d}s{\mathrm{e} }^{\mathrm{i}st}{ \|s \rangle }_{x} \bigg\} }_{t\in \mathbb{R} }$
编码	$ { \|\psi \rangle =\alpha \|0 \rangle }_{\mathrm{L}}+\beta { \|1 \rangle }_{\mathrm{L}} $$ ({ \|\alpha \|}^{2}+{ \|\beta \|}^{2}=1 $)	$\|\psi \rangle = \displaystyle\int_{-\infty }^{\infty }\mathrm{d}s\psi (s ){ \|s \rangle }_{x} \bigg(\displaystyle\int_{-\infty }^{\infty }\mathrm{d}s{ \|\psi (s ) \|}^{2}=1 \bigg)$
探测方式	光子探测	平衡零拍探测
量子逻辑门	Bit-flip: $ {\widehat{X} \|0 \rangle }_{\mathrm{L}}={ \|1 \rangle }_{\mathrm{L}}, {\widehat{X} \|1 \rangle }_{\mathrm{L}}={ \|0 \rangle }_{\mathrm{L}} $	x方向平移: $ \widehat{X} (v ){ \|s \rangle }_{x}={ \|s+v \rangle }_{x} $
	Phase-flip: $ {\widehat{Z} \|0 \rangle }_{\mathrm{L}}={ \|0 \rangle }_{\mathrm{L}}, {\widehat{Z} \|1 \rangle }_{\mathrm{L}}={- \|1 \rangle }_{\mathrm{L}} $	p方向平移: $ \widehat{Z} (u ){ \|t \rangle }_{p}={ \|t+u \rangle }_{p} $
	Hadamard门:$ {\widehat{H} \|0 \rangle }_{\mathrm{L}}={ \|+ \rangle }_{\mathrm{L}}, {\widehat{H} \|1 \rangle }_{\mathrm{L}}={ \|- \rangle }_{\mathrm{L}} $	傅立叶变换: $\widehat{R} ( {\mathrm{\pi } }/{2} ){ \|s \rangle }_{x}={ \|s \rangle }_{p}, \widehat{R} ( {\mathrm{\pi } }/{2} ){ \|t \rangle }_{p}={ \|-t \rangle }_{x}$
	可控非门: $ {\widehat{CX} \|0 \rangle }_{\mathrm{L}}{ \|0 (1 ) \rangle }_{\mathrm{L}}={ \|0 \rangle }_{\mathrm{L}}{ \|0 (1 ) \rangle }_{\mathrm{L}} $	可控X门: $ {\widehat{CX} \|{s}_{1} \rangle }_{{q}_{1}}{ \|{s}_{2} \rangle }_{{q}_{2}}={ \|{s}_{1} \rangle }_{{q}_{1}}{ \|{s}_{2}+{s}_{1} \rangle }_{{q}_{2}} $
	$ {\widehat{CX} \|1 \rangle }_{\mathrm{L}}{ \|0 (1 ) \rangle }_{\mathrm{L}}={ \|1 \rangle }_{\mathrm{L}}{ \|1 (0 ) \rangle }_{\mathrm{L}} $	$ {\widehat{CX} \|{t}_{1} \rangle }_{{p}_{1}}{ \|{t}_{2} \rangle }_{{p}_{2}}={ \|{t}_{1}-{t}_{2} \rangle }_{{p}_{1}}{ \|{t}_{2} \rangle }_{{p}_{2}} $

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