-
量子模拟利用可控性好的量子系统模拟和研究可控性差或尚不能获得的量子系统, 是量子信息科学的主要研究内容之一. 量子模拟可通过量子计算机、量子信息处理器或小型量子设备实现. 非厄米系统近二十年来受到广泛关注, 一方面是因为非厄米量子理论可作为传统厄米量子力学理论的补充和延拓, 且与开放或耗散系统联系紧密. 另一方面, 可构造具有新奇非厄米性质的量子或经典系统, 具有提高精密测量精度等应用价值. 与厄米情况相比, 非厄米量子系统的时间演化不具有幺正性, 对其开展量子模拟研究具有一定的挑战. 本文介绍了非厄米系统量子模拟理论与实验新进展. 理论方面主要介绍了基于酉算子线性组合算法, 简单梳理了各个工作的优势和局限性, 并简要介绍了量子随机行走、嵌入式和空间拓展等量子模拟理论; 实验方面简要介绍了利用核磁共振量子系统、量子光学以及利用经典系统模拟非厄米量子系统的实验. 一方面, 这些新进展结合了量子模拟与非厄米领域的研究, 推动了非厄米系统本身的理论、实验和应用发展, 另一方面拓展了量子模拟和量子计算机的可应用范围.Quantum simulation is one of the main contents of quantum information science, aiming to simulate and investigate poorly controllable or unobtainable quantum systems by using controllable quantum systems. Quantum simulation can be implemented in quantum computers, quantum simulators, and small quantum devices. Non-Hermitian systems have aroused research interest increasingly in recent two decades. On one hand, non-Hermitian quantum theories can be seen as the complex extensions of the conventional quantum mechanics, and are closely related to open systems and dissipative systems. On the other hand, both quantum systems and classical systems can be constructed as non-Hermitian systems with novel properties, which can be used to improve the precision of precise measurements. However, a non-Hermitian system is more difficult to simulate than a Hermitian system in that the time evolution of it is no longer unitary. In this review, we introduce recent research progress of quantum simulations of non-Hermitian systems. We mainly introduce theoretical researches to simulate typical non-Hermitian quantum systems by using the linear combinations of unitaries, briefly showing the advantages and limitations of each proposal, and we briefly mention other theoretical simulation methods, such as quantum random walk, space embedded and dilation. Moreover, we briefly introduce the experimental quantum simulations of non-Hermitian systems and novel phenomena in nuclear magnetic resonance, quantum optics and photonics, classical systems, etc. The recent progress of the combinations of quantum simulation and non-Hermitian physics has promoted the development of the non-Hermitian theories, experiments and applications, and expand the scope of application of quantum simulations and quantum computers.
[1] Pauli W 1943 Rev. Mod. Phys. 15 175Google Scholar
[2] Dirac P A M 1942 Proc. R. Soc. London, Ser. A 180 980Google Scholar
[3] Lee T D, Wick G C 1969 Nucl. Phys. B 9 209Google Scholar
[4] Ding P Z, Yi W 2022 Chin. Phys. B 31 010309Google Scholar
[5] Gamow G 1928 Zeitschrift für Physik 51 204Google Scholar
[6] Moiseyev N 2011 Non-Hermitian Quantum Mechanics (Cambridge: Cambridge University Press) pp211–247
[7] Breuer H P, Petruccione F 2002 The Theory of Open Quantum Systems (10th Anniversary Ed.) (Oxford: Oxford University Press) pp421–431
[8] Barreiro J T, Müller M, Schindler P, Nigg D, Monz T, Chwalla M, Hennrich M, Roos C F, Zoller P, Blatt R 2011 Nature 470 486Google Scholar
[9] Hu Z, Xia R, Kais S A 2020 Sci. Rep. 10 3301Google Scholar
[10] Del Re L, Rost B, Kemper A F, Freericks J K 2020 Phys. Rev. B 102 125112Google Scholar
[11] Viyuela O, Rivas A, Gasparinetti S, Wallraff A, Filipp S, Martin-Delgado M A 2018 npj Quantum Inf. 4 10Google Scholar
[12] Schlimgen A W, Head-Marsden K, Sager L M, Narang P, Mazziotti D A 2021 Phys. Rev. Lett. 127 270503Google Scholar
[13] Del Re L, Rost B, Foss-Feig M, Kemper A F, Freericks J K 2022 arXiv: 2204.12400[quant-ph]
[14] Zheng C 2021 Sci. Rep. 11 3960Google Scholar
[15] 陈曾军, 宁西京 2003 物理学报 52 2683Google Scholar
Chen Z J, Ning X J 2003 Acta Phys. Sin. 52 2683Google Scholar
[16] Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243Google Scholar
[17] Bender C M, Brody D C, Jones H F 2004 Phys. Rev. D 70 025001Google Scholar
[18] Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401Google Scholar
[19] Bender C M 2007 Rep. Prog. Phys. 70 947Google Scholar
[20] Mostafazadeh A 2002 J. Math. Phys. 43 205Google Scholar
[21] Mostafazadeh A 1998 J. Math. Phys. 39 4499Google Scholar
[22] Mostafazadeh A 2002 J. Math. Phys. 43 2814Google Scholar
[23] Mostafazadeh A 2002 Nucl. Phys. B 640 419Google Scholar
[24] Mostafazadeh A 2004 J. Math. Phys. 45 932Google Scholar
[25] Deutsch M 1985 Proc. R. Soc. London Ser. A 400 97Google Scholar
[26] Jin L, Song Z 2009 Phys. Rev. A 80 052107Google Scholar
[27] 唐原江, 梁超, 刘永椿 2022 物理学报 71 171101Google Scholar
Tang Y J, Liang C, Liu Y C 2022 Acta Phys. Sin. 71 171101Google Scholar
[28] 张禧征, 王鹏, 张坤亮, 杨学敏, 宋智 2022 物理学报 71 174501Google Scholar
Zhang, X Z, Wang P, Zhang K L, Yang X M, Song Z 2022 Acta Phys. Sin. 71 174501Google Scholar
[29] Kato T 1966 Perturbation Theory for Linear Operators (Berlin: Springer-Verlag) pp64–516
[30] Heiss W D 2012 J. Phys. A: Math. Theor. 45 444016Google Scholar
[31] Regensburger A, Bersch C, Miri M A, Onishchukov G, Christodoulides D N, Peschel U 2012 Nature 488 167Google Scholar
[32] Hodaei H, Hassan A U, Wittek S, Garcia-Gracia H, El-Ganainy R, Christodoulides D N, Khajavikhan M 2017 Nature 548 187Google Scholar
[33] Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192Google Scholar
[34] Wimmer M, Miri M A, Christodoulides D N, Peschel U 2015 Sci. Rep. 5 17760Google Scholar
[35] Feng L, Xu Y L, Fegadolli W S, Lu M H, Oliveira J E B, Almeida V R, Chen Y F, Scherer A 2013 Nat. Mater. 12 108Google Scholar
[36] Xu H, Mason D, Jiang L, Harris J G E 2016 Nature 537 80Google Scholar
[37] Yao R Z, Lee C, Podolskiy V, Guo W 2018 Laser Photonics Rev. 13 1800154Google Scholar
[38] Zheng C, Li D 2022 Sci. Rep. 12 2824Google Scholar
[39] Li D, Zheng C 2022 Entropy 2 4Google Scholar
[40] 李丽娟, 明飞, 宋学科, 叶柳, 王栋 2022 物理学报 71 070302Google Scholar
Li L J, Ming F, Song X K, Wang D 2022 Acta Phys. Sin. 71 070302Google Scholar
[41] Feynman R P 1982 Int. J. Theor. Phys. 21 467Google Scholar
[42] Greiner M, Mandel O, Esslinger T, Hansch T W, Bloch I 2002 Nature 415 39Google Scholar
[43] Gerritsma R, Kirchmair G, Zahringer F, Solano E, Blatt R, Roos C F 2010 Nature 463 68Google Scholar
[44] Pearson J, Feng G R, Zheng C, Long G L 2016 Sci. China Phys. Mech. Astron. 59 120312Google Scholar
[45] Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025Google Scholar
[46] Georgescu I M, Ashhab S, Nori F 2014 Nature 86 153Google Scholar
[47] Zheng C, Hao L, Long G L 2013 Philol. Trans. R. Soc. A 371 20120053Google Scholar
[48] Gao T, Estrecho E, Bliokh K Y, Liew T C H, Fraser M D, Brodbeck S, Kamp M, Schneider C, Hofling S, Yamamoto Y 2015 Nature 526 554Google Scholar
[49] Zheng C, Wei S 2018 Int. J. Theor. Phys. 57 2203Google Scholar
[50] Wang H, Wei S, Zheng C, Kong X, Wen J, Nie X, Li J, Lu D, Xin T 2020 Phys. Rev. A 102 012610Google Scholar
[51] Zheng C 2018 EPL 123 40002Google Scholar
[52] Wen J, Zheng C, Kong X, Wei S, Xin T, Long G 2019 Phys. Rev. A 99 062122Google Scholar
[53] Li C, Wang P, Jin L, Song Z 2021 J. Phys. Commun. 5 105011Google Scholar
[54] Jin L 2022 Chin. Phys. Lett. 39 037302Google Scholar
[55] Zheng C 2019 EPL 126 30005Google Scholar
[56] Wen J, Qin G, Zheng C, Wei S, Kong X, Xin T, Long G 2020 npj Quantum Inf. 6 28Google Scholar
[57] Zheng C 2022 Chin. Phys. B 31 100301Google Scholar
[58] Joglekar Y N, Saxena A 2011 Phys. Rev. A 83 050101Google Scholar
[59] Valle G D, Longhi S 2013 Phys. Rev. A 87 022119Google Scholar
[60] Faisal F H M, Moloney J V 1981 J. Phys. B 14 3603Google Scholar
[61] Zhang S, Jin L, Song Z 2022 Chin. Phys. B 31 010312Google Scholar
[62] Jin L, Song Z 2010 Phys. Rev. A 81 032109Google Scholar
[63] 胡洲, 曾招云, 唐佳, 罗小兵 2022 物理学报 71 074207Google Scholar
Hu Z, Zeng Z Y, Tang J, Luo X B 2022 Acta Phys. Sin. 71 074207Google Scholar
[64] Cannata F, Junker G, Trost J 1998 Phys. Lett. A 246 219Google Scholar
[65] Chuang Y L, Ziauddin, Lee R K 2018 Opt. Express 26 17Google Scholar
[66] Benioff P 1980 J. Stat. Phys. 22 563Google Scholar
[67] [68] [69] 范桁 2018 物理学报 67 120301Google Scholar
Fan H 2018 Acta Phys. Sin 67 120301Google Scholar
[70] Garcia-Perez G, Rossi M A C, Maniscalco S 2020 npj Quantum Inf. 6 1Google Scholar
[71] Wei S J, Ruan D, Long G L 2016 Sci. Rep. 6 30727Google Scholar
[72] Long G L 2006 Commun. Theor. Phys. 45 825Google Scholar
[73] Long G L 2011 Int. J. Theor. Phys. 50 1305Google Scholar
[74] Motta M, Sun C, Tan A T K, O’Rourke M J, Ye E, Minnich A J, Brandao F G S L, Chan G K L 2020 Nat. Phys. 16 205Google Scholar
[75] Kamakari H, Sun S N, Motta M, Minnich A J 2022 PRX Quantum 3 010320Google Scholar
[76] Endo S, Sun J, Li Y, Benjamin S C, Yuan X 2020 Phys. Rev. Lett. 125 010501Google Scholar
[77] Head-Marsden K, Krastanov S, Mazziotti D A, Narang P 2021 Phys. Rev. Res. 3 013182Google Scholar
[78] Hu Z, Head-Marsden K, Mazziotti D A, Narang P, Kais S 2022 Quantum 6 726Google Scholar
[79] Gudder S 2007 Quantum Inf. Process. 6 37Google Scholar
[80] Long G L, Liu Y 2008 Commun. Theor. Phys. 50 1303Google Scholar
[81] Long G L, Liu Y, Wang C 2009 Commun. Theor. Phys. 51 65Google Scholar
[82] Long G L 2007 Quantum Inf. Process. 6 49Google Scholar
[83] Cao H X, Long G L, Guo Z H 2013 Int. J. Theor. Phys. 52 1Google Scholar
[84] Cui J X, Zhou T, Long G L 2012 Quantum Inf. Process. 11 317Google Scholar
[85] Nielsen M A, Chuang I L 2002 Am. J. Phys. 70 558Google Scholar
[86] Penrose R 1971 Quantum Theory and Beyond (Cambridge: Cambridge University Press) pp151–180
[87] Wen J W, Zheng C, Ye Z D, Xin T, Long G L 2021 Phys. Rev. Res. 3 013256Google Scholar
[88] Li X G, Zheng C, Gao J C, Long G L 2022 Phys. Rev. A 105 032405Google Scholar
[89] Shao C, Li Y, Li H 2019 J. Syst. Sci. Complex 32 375Google Scholar
[90] Günther N, Samsonov B F 2008 Phys. Rev. Lett. 101 230404Google Scholar
[91] Xiao L, Zhan X, Bian Z H, Wang K K, Zhang X, Wang X P, Li J, Mochizuki K, Kim D, Kawakami N, Yi W, Obuse H, Sanders B C, Xue P 2017 Nat. Phys. 13 1117Google Scholar
[92] Choi Y, Hahn C, Yoon J, Song S 2018 Nat. Commun. 9 2182Google Scholar
[93] Ge L, Tureci H E 2013 Phys. Rev. A 88 053810Google Scholar
[94] Yang F, Liu Y C, You L 2017 Phys. Rev. A 96 053845Google Scholar
[95] Li Y, Peng Y G, Han L, Miri M A, Li W, Xiao M, Zhu X F, Zhao J, Alu A, Fan S, Qiu C W 2019 Science 364 170Google Scholar
[96] Xu H S, Jin L 2021 Phys. Rev. A 104 012218Google Scholar
[97] Gao P, Sun Y, Liu X, Wang T, Wang C 2019 IEEE Access 7 107874Google Scholar
[98] Longhi S, Pinotti E 2019 EPL 125 10006Google Scholar
[99] Zheng C 2021 EPL 136 30002Google Scholar
[100] Zheng C 2022 Entropy 24 867Google Scholar
[101] Zheng C, Tian J, Li D L, Wen J W, Wei S J, Li Y S 2020 Entropy 22 812Google Scholar
[102] Gao W C, Zheng C, Liu L, Wang T J, Wang C 2021 Opt. Express 29 517Google Scholar
[103] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687Google Scholar
[104] Farhi E, Gutmann S 1998 Phys. Rev. A 58 915Google Scholar
[105] Watrous J 2001 J. Comput. Syst. Sci. 62 376Google Scholar
[106] Xue P, Zhang R, Qin H, Zhan X, Bian Z H, Li J, Sanders B C 2015 Phys. Rev. Lett. 114 140502Google Scholar
[107] Casanova J, Sabín C, León J, Egusquiza I L, Gerritsma R, Roos C F, García-Ripoll J J, Solano E 2011 Phys. Rev. X 1 021018Google Scholar
[108] Candia R D, Mejia B, Castillo H, Pedernales J S, Casanova J, Solano E 2013 Phys. Rev. Lett. 111 240502Google Scholar
[109] Alvarez-Rodriguez U, Casanova J, Lamata L, Solano E 2013 Phys. Rev. Lett. 111 090503Google Scholar
[110] Zhang X, Shen Y, Zhang J, Casanova J, Lamata L, Solano E, Yung M H, Zhang J N, Kim K 2015 Nat. Commun. 6 7917Google Scholar
[111] Keil R, Noh C, Rai A, Stützer S, Nolte S, Angelakis D G, Szameit A 2015 Optica 2 454Google Scholar
[112] Pedernales J S, Candia R D, Schindler P, Monz T, Hennrich M, Casanova J, Solano E 2014 Phys. Rev. A 90 012327Google Scholar
[113] Huang M, Kumar A, Wu J 2018 Phys. Lett. A 382 2578Google Scholar
[114] 黄旻怡 2018 博士学位论文 (杭州: 浙江大学)
Huang M 2018 Ph. D. Dissertation (Hang zhou: Zhejiang University) (in Chines)
[115] Beneduci R 2020 J. Phys.: Conf. Ser. 1638 012006Google Scholar
[116] Bender C M, Brody D C, Jones H F, Meister B K 2007 Phys. Rev. Lett. 98 040403Google Scholar
[117] Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland) pp127–140
[118] 孔祥宇, 朱垣晔, 闻经纬, 辛涛, 李可仁, 龙桂鲁 2018 物理学报 68 220301Google Scholar
Kong X Y, Zhu Y Y, Wen J W, Xin T, Li K R, Long G L 2018 Acta Opt. Sin. 68 220301Google Scholar
[119] Long G L, Qin W, Yang Z, Li J L 2018 Sci. China: Phys. Mech. Astron. 61 030311Google Scholar
[120] Xin T, Li H, Wang B X, Long G L 2015 Phys. Rev. A 92 022126Google Scholar
[121] Peng X, Du J, Suter D 2005 Phys. Rev. A 71 012307Google Scholar
[122] Zhang J, Peng X, Rajendran N, Suter D 2008 Phys. Rev. Lett. 100 100501Google Scholar
[123] Feng G R, Lu Y, Hao L, Zhang F H, Long G L 2013 Sci. Rep. 3 2232Google Scholar
[124] Gunther N, Samsonov B F 2008 Phys. Rev. A 78 042115Google Scholar
[125] O’Neill P 2013 Dev. Growth Differ. 55 188Google Scholar
[126] Wiltschko W, Wiltschko R 1972 Science 176 62Google Scholar
[127] Ritz T, Thalau P, Phillips J B, Wiltschko R, Wiltschko W 2004 Nature 429 177Google Scholar
[128] Thalau P, Ritz T, Stapput K, Wiltschko R, Wiltschko W 2005 Naturwissenschaften 92 86Google Scholar
[129] Biskup T, Schleicher E, Okafuji A, Link G, Hitomi K, Getzoff E D, Weber S 2009 Angew. Chem. Int. Ed. 48 404Google Scholar
[130] Wiltschko W, Stapput K, Thalau P, Wiltschko R 2006 Naturwissenschaften 93 300Google Scholar
[131] Vandersypen L M K, Chuang I L 2005 Rev. Mod. Phys. 76 1037Google Scholar
[132] Han M, Huang W, Ma Y 2007 Int. J. Mod. Phys. D 16 1397Google Scholar
[133] Li K, Li Y N, Han M X, Lu S R, Zhou J, Ruan D, Long G L, Wan Y D, Lu D W, Zeng B, Laflamme R 2019 Commun. Phys. 2 122Google Scholar
[134] Rovelli C, Vidotto F 2014 Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory. Cambridge Monographs on Mathematical Physics (Cambridge: Cambridge University Press) pp3–27
[135] Perez A 2013 Living Rev. Rel. 16 3Google Scholar
[136] Tennant D A, Perring T G, Cowley R A, Nagler S E 1993 Phys. Rev. Lett. 70 4003Google Scholar
[137] Tennant D A, Cowley R A, Nagler S E, Tsvelik A M 1995 Phys. Rev. B 52 13368Google Scholar
[138] Liao Y A, Rittner A S C, Paprotta T, Li W, Partridge G B, Hulet R F, Baur S K, Mueller E J 2010 Nature 467 567Google Scholar
[139] Zheng C, Song S Y, Li J L, Long G L 2013 J. Opt. Soc. Am. B 30 1688Google Scholar
[140] Hu S W, Xue K, Ge M L 2008 Phys. Rev. A 78 022319Google Scholar
[141] Peterson J P S, Batalhão T B, Herrera M, Souza A M, Sarthour R S, Oliveira I S, Serra R M 2019 Phys. Rev. Lett. 123 240601Google Scholar
[142] Klatzow J, Becker J N, Ledingham P M, Weinzetl C, Kaczmarek K T, Saunders D J, Nunn J, Walmsley I A, Uzdin R, Poem E 2019 Phys. Rev. Lett. 122 110601Google Scholar
[143] Nielsen M A, Chuang I L 2011 Quantum Computation and Quantum Information (10th Ed.) (New York: Cambridge University Press) pp416–561
[144] Salles A, de Melo F, Almeida M P, Hor-Meyll M, Walborn S P, Souto Ribeiro P H, Davidovich L 2008 Phys. Rev. A 78 022322Google Scholar
[145] Passos M H M, Santos Alan C, Sarandy Marcelo S, Huguenin J A O 2019 Phys. Rev. A 100 022113Google Scholar
[146] Xiao L, Wang K K, Zhan X, Bian Z H, Kawabata K, Ueda M, Yi W, Xue P 2019 Phys. Rev. Lett. 123 230401Google Scholar
[147] Lima G, Vargas A, Neves L, Guzmán R, Saavedra C 2009 Opt. Express 17 10688Google Scholar
[148] Machado P, Matoso A A, Barros M R, Neves L, Pádua S 2019 Phys. Rev. A 99 063839Google Scholar
[149] de Assis P L, Carvalho M A D, Berruezo L P, Ferraz J, Santos I F, Sciarrino F, Pádua S 2011 Opt. Express 19 3715Google Scholar
[150] Baldijão R D, Borges G F, Marques B, Solís-Prosser M A, Neves L, Pádua S 2017 Phys. Rev. A 96 032329Google Scholar
[151] Borges G F, Baldijão R D, CondáJ G L, Cabral J S, Marques B, Terra Cunha M, Cabello A, Pádua S 2018 Phys. Rev. A 97 022301Google Scholar
[152] Cardoso A C, CondéJ G L, Marques B, Cabral J S, Pádua S 2021 Phys. Rev. A 103 013722Google Scholar
[153] Maraviglia N, Yard P, Wakefield R, Carolan J, Sparrow C, Chakhmakhchyan L, Harrold C, Hashimoto T, Matsuda N, Harter A K, Joglekar Y N, Laing A 2022 Phys. Rev. Res. 4 013051Google Scholar
[154] Schindler J, Li A, Zheng M C, Ellis F M, Kottos T 2011 Phys. Rev. A 84 040101Google Scholar
[155] Lin Z, Schindler J, Ellis F M, Kottos T 2012 Phys. Rev. A 85 050101Google Scholar
[156] 傅廷, 王宇飞, 王学友, 陈静瑄, 周旭彦, 郑婉华 2021 中国激光 48 1201005Google Scholar
Fu T, Wang Y F, Wang X Y, Chen J X, Zhou X Y, Zheng W H 2021 Chinese Journal of Lasers 48 1201005Google Scholar
[157] El-Ganainy R, Makris K G, Christodoulides D N, Musslimani Z H 2007 Opt. Lett. 32 002632Google Scholar
[158] Miri M, LiKamWa P, Christodoulides D N 2012 Opt. Lett. 37 000764Google Scholar
[159] Hodaei H, Miri M, Heinrich M, Christodoulides D N, Khajavikhan M 2014 SPIE Process. 9162 91621QGoogle Scholar
[160] Feng L, Wong Z J, Ma R M, Wang Y, Zhang X 2014 Science 346 972Google Scholar
[161] Gu Z Y, Zhang N, Lyu Q, Li M, Xiao S M, Song Q H 2016 Laser Photonics Rev. 10 588Google Scholar
[162] Miao P, Zhang Z, Sun J, Walasik W, Longhi S, Litchinitser N M, Feng L 2016 Science 353 464Google Scholar
[163] Zhang Z F, Qiao X D, Midya B, Liu K, Sun J B, Wu T W, Liu W J, Agarwal R, Jornet J M, Longhi S, Litchinitser N M, Feng L 2020 Science 368 760Google Scholar
[164] Xu H S, Jin L 2022 Phys. Rev. Res. 4 L032015Google Scholar
[165] Jin L, Song Z 2018 Phys. Rev. Lett. 121 073901Google Scholar
[166] 成恩宏, 郎利君 2022 物理学报 71 160301Google Scholar
Chen E H, Lang L J 2022 Acta Phys. Sin. 71 160301Google Scholar
-
图 6 量子计算机的流程图和量子线路图 (a)模拟广义APT系统的流程图; (b)模拟广义APT系统的线路图; (c)第一次测量之后的初始化和空间准备的量子线路图; (d)第二次测量之后的量子线路图[55]
Fig. 6. Flow chart and quantum circuit for a qubit computer: (a) Flow chart of quantum simulation of the generalized APT-symmetric system; (b) quantum circuit to simulate the evolution of the generalized APT-symmetric system; (c) quantum circuit for space preparation and initialization after the first measurement; (d) quantum circuit for initialization after the second measurement[55]
图 15 量子时空和四面体 (a)静态四维(4D) 量子时空; (b)五价点的动态量子时空; (c) S 3 的局域结构; (d)量子几何四面体[133]
Fig. 15. Quantum spacetime and tetrahedra: (a) A static 4D quantum spacetime; (b) a dynamical quantum spacetime with a number of five valent vertices; (c) the local structure of S 3; (d) quantum geometrical tetrahedra[133]
-
[1] Pauli W 1943 Rev. Mod. Phys. 15 175Google Scholar
[2] Dirac P A M 1942 Proc. R. Soc. London, Ser. A 180 980Google Scholar
[3] Lee T D, Wick G C 1969 Nucl. Phys. B 9 209Google Scholar
[4] Ding P Z, Yi W 2022 Chin. Phys. B 31 010309Google Scholar
[5] Gamow G 1928 Zeitschrift für Physik 51 204Google Scholar
[6] Moiseyev N 2011 Non-Hermitian Quantum Mechanics (Cambridge: Cambridge University Press) pp211–247
[7] Breuer H P, Petruccione F 2002 The Theory of Open Quantum Systems (10th Anniversary Ed.) (Oxford: Oxford University Press) pp421–431
[8] Barreiro J T, Müller M, Schindler P, Nigg D, Monz T, Chwalla M, Hennrich M, Roos C F, Zoller P, Blatt R 2011 Nature 470 486Google Scholar
[9] Hu Z, Xia R, Kais S A 2020 Sci. Rep. 10 3301Google Scholar
[10] Del Re L, Rost B, Kemper A F, Freericks J K 2020 Phys. Rev. B 102 125112Google Scholar
[11] Viyuela O, Rivas A, Gasparinetti S, Wallraff A, Filipp S, Martin-Delgado M A 2018 npj Quantum Inf. 4 10Google Scholar
[12] Schlimgen A W, Head-Marsden K, Sager L M, Narang P, Mazziotti D A 2021 Phys. Rev. Lett. 127 270503Google Scholar
[13] Del Re L, Rost B, Foss-Feig M, Kemper A F, Freericks J K 2022 arXiv: 2204.12400[quant-ph]
[14] Zheng C 2021 Sci. Rep. 11 3960Google Scholar
[15] 陈曾军, 宁西京 2003 物理学报 52 2683Google Scholar
Chen Z J, Ning X J 2003 Acta Phys. Sin. 52 2683Google Scholar
[16] Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243Google Scholar
[17] Bender C M, Brody D C, Jones H F 2004 Phys. Rev. D 70 025001Google Scholar
[18] Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401Google Scholar
[19] Bender C M 2007 Rep. Prog. Phys. 70 947Google Scholar
[20] Mostafazadeh A 2002 J. Math. Phys. 43 205Google Scholar
[21] Mostafazadeh A 1998 J. Math. Phys. 39 4499Google Scholar
[22] Mostafazadeh A 2002 J. Math. Phys. 43 2814Google Scholar
[23] Mostafazadeh A 2002 Nucl. Phys. B 640 419Google Scholar
[24] Mostafazadeh A 2004 J. Math. Phys. 45 932Google Scholar
[25] Deutsch M 1985 Proc. R. Soc. London Ser. A 400 97Google Scholar
[26] Jin L, Song Z 2009 Phys. Rev. A 80 052107Google Scholar
[27] 唐原江, 梁超, 刘永椿 2022 物理学报 71 171101Google Scholar
Tang Y J, Liang C, Liu Y C 2022 Acta Phys. Sin. 71 171101Google Scholar
[28] 张禧征, 王鹏, 张坤亮, 杨学敏, 宋智 2022 物理学报 71 174501Google Scholar
Zhang, X Z, Wang P, Zhang K L, Yang X M, Song Z 2022 Acta Phys. Sin. 71 174501Google Scholar
[29] Kato T 1966 Perturbation Theory for Linear Operators (Berlin: Springer-Verlag) pp64–516
[30] Heiss W D 2012 J. Phys. A: Math. Theor. 45 444016Google Scholar
[31] Regensburger A, Bersch C, Miri M A, Onishchukov G, Christodoulides D N, Peschel U 2012 Nature 488 167Google Scholar
[32] Hodaei H, Hassan A U, Wittek S, Garcia-Gracia H, El-Ganainy R, Christodoulides D N, Khajavikhan M 2017 Nature 548 187Google Scholar
[33] Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192Google Scholar
[34] Wimmer M, Miri M A, Christodoulides D N, Peschel U 2015 Sci. Rep. 5 17760Google Scholar
[35] Feng L, Xu Y L, Fegadolli W S, Lu M H, Oliveira J E B, Almeida V R, Chen Y F, Scherer A 2013 Nat. Mater. 12 108Google Scholar
[36] Xu H, Mason D, Jiang L, Harris J G E 2016 Nature 537 80Google Scholar
[37] Yao R Z, Lee C, Podolskiy V, Guo W 2018 Laser Photonics Rev. 13 1800154Google Scholar
[38] Zheng C, Li D 2022 Sci. Rep. 12 2824Google Scholar
[39] Li D, Zheng C 2022 Entropy 2 4Google Scholar
[40] 李丽娟, 明飞, 宋学科, 叶柳, 王栋 2022 物理学报 71 070302Google Scholar
Li L J, Ming F, Song X K, Wang D 2022 Acta Phys. Sin. 71 070302Google Scholar
[41] Feynman R P 1982 Int. J. Theor. Phys. 21 467Google Scholar
[42] Greiner M, Mandel O, Esslinger T, Hansch T W, Bloch I 2002 Nature 415 39Google Scholar
[43] Gerritsma R, Kirchmair G, Zahringer F, Solano E, Blatt R, Roos C F 2010 Nature 463 68Google Scholar
[44] Pearson J, Feng G R, Zheng C, Long G L 2016 Sci. China Phys. Mech. Astron. 59 120312Google Scholar
[45] Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025Google Scholar
[46] Georgescu I M, Ashhab S, Nori F 2014 Nature 86 153Google Scholar
[47] Zheng C, Hao L, Long G L 2013 Philol. Trans. R. Soc. A 371 20120053Google Scholar
[48] Gao T, Estrecho E, Bliokh K Y, Liew T C H, Fraser M D, Brodbeck S, Kamp M, Schneider C, Hofling S, Yamamoto Y 2015 Nature 526 554Google Scholar
[49] Zheng C, Wei S 2018 Int. J. Theor. Phys. 57 2203Google Scholar
[50] Wang H, Wei S, Zheng C, Kong X, Wen J, Nie X, Li J, Lu D, Xin T 2020 Phys. Rev. A 102 012610Google Scholar
[51] Zheng C 2018 EPL 123 40002Google Scholar
[52] Wen J, Zheng C, Kong X, Wei S, Xin T, Long G 2019 Phys. Rev. A 99 062122Google Scholar
[53] Li C, Wang P, Jin L, Song Z 2021 J. Phys. Commun. 5 105011Google Scholar
[54] Jin L 2022 Chin. Phys. Lett. 39 037302Google Scholar
[55] Zheng C 2019 EPL 126 30005Google Scholar
[56] Wen J, Qin G, Zheng C, Wei S, Kong X, Xin T, Long G 2020 npj Quantum Inf. 6 28Google Scholar
[57] Zheng C 2022 Chin. Phys. B 31 100301Google Scholar
[58] Joglekar Y N, Saxena A 2011 Phys. Rev. A 83 050101Google Scholar
[59] Valle G D, Longhi S 2013 Phys. Rev. A 87 022119Google Scholar
[60] Faisal F H M, Moloney J V 1981 J. Phys. B 14 3603Google Scholar
[61] Zhang S, Jin L, Song Z 2022 Chin. Phys. B 31 010312Google Scholar
[62] Jin L, Song Z 2010 Phys. Rev. A 81 032109Google Scholar
[63] 胡洲, 曾招云, 唐佳, 罗小兵 2022 物理学报 71 074207Google Scholar
Hu Z, Zeng Z Y, Tang J, Luo X B 2022 Acta Phys. Sin. 71 074207Google Scholar
[64] Cannata F, Junker G, Trost J 1998 Phys. Lett. A 246 219Google Scholar
[65] Chuang Y L, Ziauddin, Lee R K 2018 Opt. Express 26 17Google Scholar
[66] Benioff P 1980 J. Stat. Phys. 22 563Google Scholar
[67] [68] [69] 范桁 2018 物理学报 67 120301Google Scholar
Fan H 2018 Acta Phys. Sin 67 120301Google Scholar
[70] Garcia-Perez G, Rossi M A C, Maniscalco S 2020 npj Quantum Inf. 6 1Google Scholar
[71] Wei S J, Ruan D, Long G L 2016 Sci. Rep. 6 30727Google Scholar
[72] Long G L 2006 Commun. Theor. Phys. 45 825Google Scholar
[73] Long G L 2011 Int. J. Theor. Phys. 50 1305Google Scholar
[74] Motta M, Sun C, Tan A T K, O’Rourke M J, Ye E, Minnich A J, Brandao F G S L, Chan G K L 2020 Nat. Phys. 16 205Google Scholar
[75] Kamakari H, Sun S N, Motta M, Minnich A J 2022 PRX Quantum 3 010320Google Scholar
[76] Endo S, Sun J, Li Y, Benjamin S C, Yuan X 2020 Phys. Rev. Lett. 125 010501Google Scholar
[77] Head-Marsden K, Krastanov S, Mazziotti D A, Narang P 2021 Phys. Rev. Res. 3 013182Google Scholar
[78] Hu Z, Head-Marsden K, Mazziotti D A, Narang P, Kais S 2022 Quantum 6 726Google Scholar
[79] Gudder S 2007 Quantum Inf. Process. 6 37Google Scholar
[80] Long G L, Liu Y 2008 Commun. Theor. Phys. 50 1303Google Scholar
[81] Long G L, Liu Y, Wang C 2009 Commun. Theor. Phys. 51 65Google Scholar
[82] Long G L 2007 Quantum Inf. Process. 6 49Google Scholar
[83] Cao H X, Long G L, Guo Z H 2013 Int. J. Theor. Phys. 52 1Google Scholar
[84] Cui J X, Zhou T, Long G L 2012 Quantum Inf. Process. 11 317Google Scholar
[85] Nielsen M A, Chuang I L 2002 Am. J. Phys. 70 558Google Scholar
[86] Penrose R 1971 Quantum Theory and Beyond (Cambridge: Cambridge University Press) pp151–180
[87] Wen J W, Zheng C, Ye Z D, Xin T, Long G L 2021 Phys. Rev. Res. 3 013256Google Scholar
[88] Li X G, Zheng C, Gao J C, Long G L 2022 Phys. Rev. A 105 032405Google Scholar
[89] Shao C, Li Y, Li H 2019 J. Syst. Sci. Complex 32 375Google Scholar
[90] Günther N, Samsonov B F 2008 Phys. Rev. Lett. 101 230404Google Scholar
[91] Xiao L, Zhan X, Bian Z H, Wang K K, Zhang X, Wang X P, Li J, Mochizuki K, Kim D, Kawakami N, Yi W, Obuse H, Sanders B C, Xue P 2017 Nat. Phys. 13 1117Google Scholar
[92] Choi Y, Hahn C, Yoon J, Song S 2018 Nat. Commun. 9 2182Google Scholar
[93] Ge L, Tureci H E 2013 Phys. Rev. A 88 053810Google Scholar
[94] Yang F, Liu Y C, You L 2017 Phys. Rev. A 96 053845Google Scholar
[95] Li Y, Peng Y G, Han L, Miri M A, Li W, Xiao M, Zhu X F, Zhao J, Alu A, Fan S, Qiu C W 2019 Science 364 170Google Scholar
[96] Xu H S, Jin L 2021 Phys. Rev. A 104 012218Google Scholar
[97] Gao P, Sun Y, Liu X, Wang T, Wang C 2019 IEEE Access 7 107874Google Scholar
[98] Longhi S, Pinotti E 2019 EPL 125 10006Google Scholar
[99] Zheng C 2021 EPL 136 30002Google Scholar
[100] Zheng C 2022 Entropy 24 867Google Scholar
[101] Zheng C, Tian J, Li D L, Wen J W, Wei S J, Li Y S 2020 Entropy 22 812Google Scholar
[102] Gao W C, Zheng C, Liu L, Wang T J, Wang C 2021 Opt. Express 29 517Google Scholar
[103] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687Google Scholar
[104] Farhi E, Gutmann S 1998 Phys. Rev. A 58 915Google Scholar
[105] Watrous J 2001 J. Comput. Syst. Sci. 62 376Google Scholar
[106] Xue P, Zhang R, Qin H, Zhan X, Bian Z H, Li J, Sanders B C 2015 Phys. Rev. Lett. 114 140502Google Scholar
[107] Casanova J, Sabín C, León J, Egusquiza I L, Gerritsma R, Roos C F, García-Ripoll J J, Solano E 2011 Phys. Rev. X 1 021018Google Scholar
[108] Candia R D, Mejia B, Castillo H, Pedernales J S, Casanova J, Solano E 2013 Phys. Rev. Lett. 111 240502Google Scholar
[109] Alvarez-Rodriguez U, Casanova J, Lamata L, Solano E 2013 Phys. Rev. Lett. 111 090503Google Scholar
[110] Zhang X, Shen Y, Zhang J, Casanova J, Lamata L, Solano E, Yung M H, Zhang J N, Kim K 2015 Nat. Commun. 6 7917Google Scholar
[111] Keil R, Noh C, Rai A, Stützer S, Nolte S, Angelakis D G, Szameit A 2015 Optica 2 454Google Scholar
[112] Pedernales J S, Candia R D, Schindler P, Monz T, Hennrich M, Casanova J, Solano E 2014 Phys. Rev. A 90 012327Google Scholar
[113] Huang M, Kumar A, Wu J 2018 Phys. Lett. A 382 2578Google Scholar
[114] 黄旻怡 2018 博士学位论文 (杭州: 浙江大学)
Huang M 2018 Ph. D. Dissertation (Hang zhou: Zhejiang University) (in Chines)
[115] Beneduci R 2020 J. Phys.: Conf. Ser. 1638 012006Google Scholar
[116] Bender C M, Brody D C, Jones H F, Meister B K 2007 Phys. Rev. Lett. 98 040403Google Scholar
[117] Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland) pp127–140
[118] 孔祥宇, 朱垣晔, 闻经纬, 辛涛, 李可仁, 龙桂鲁 2018 物理学报 68 220301Google Scholar
Kong X Y, Zhu Y Y, Wen J W, Xin T, Li K R, Long G L 2018 Acta Opt. Sin. 68 220301Google Scholar
[119] Long G L, Qin W, Yang Z, Li J L 2018 Sci. China: Phys. Mech. Astron. 61 030311Google Scholar
[120] Xin T, Li H, Wang B X, Long G L 2015 Phys. Rev. A 92 022126Google Scholar
[121] Peng X, Du J, Suter D 2005 Phys. Rev. A 71 012307Google Scholar
[122] Zhang J, Peng X, Rajendran N, Suter D 2008 Phys. Rev. Lett. 100 100501Google Scholar
[123] Feng G R, Lu Y, Hao L, Zhang F H, Long G L 2013 Sci. Rep. 3 2232Google Scholar
[124] Gunther N, Samsonov B F 2008 Phys. Rev. A 78 042115Google Scholar
[125] O’Neill P 2013 Dev. Growth Differ. 55 188Google Scholar
[126] Wiltschko W, Wiltschko R 1972 Science 176 62Google Scholar
[127] Ritz T, Thalau P, Phillips J B, Wiltschko R, Wiltschko W 2004 Nature 429 177Google Scholar
[128] Thalau P, Ritz T, Stapput K, Wiltschko R, Wiltschko W 2005 Naturwissenschaften 92 86Google Scholar
[129] Biskup T, Schleicher E, Okafuji A, Link G, Hitomi K, Getzoff E D, Weber S 2009 Angew. Chem. Int. Ed. 48 404Google Scholar
[130] Wiltschko W, Stapput K, Thalau P, Wiltschko R 2006 Naturwissenschaften 93 300Google Scholar
[131] Vandersypen L M K, Chuang I L 2005 Rev. Mod. Phys. 76 1037Google Scholar
[132] Han M, Huang W, Ma Y 2007 Int. J. Mod. Phys. D 16 1397Google Scholar
[133] Li K, Li Y N, Han M X, Lu S R, Zhou J, Ruan D, Long G L, Wan Y D, Lu D W, Zeng B, Laflamme R 2019 Commun. Phys. 2 122Google Scholar
[134] Rovelli C, Vidotto F 2014 Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory. Cambridge Monographs on Mathematical Physics (Cambridge: Cambridge University Press) pp3–27
[135] Perez A 2013 Living Rev. Rel. 16 3Google Scholar
[136] Tennant D A, Perring T G, Cowley R A, Nagler S E 1993 Phys. Rev. Lett. 70 4003Google Scholar
[137] Tennant D A, Cowley R A, Nagler S E, Tsvelik A M 1995 Phys. Rev. B 52 13368Google Scholar
[138] Liao Y A, Rittner A S C, Paprotta T, Li W, Partridge G B, Hulet R F, Baur S K, Mueller E J 2010 Nature 467 567Google Scholar
[139] Zheng C, Song S Y, Li J L, Long G L 2013 J. Opt. Soc. Am. B 30 1688Google Scholar
[140] Hu S W, Xue K, Ge M L 2008 Phys. Rev. A 78 022319Google Scholar
[141] Peterson J P S, Batalhão T B, Herrera M, Souza A M, Sarthour R S, Oliveira I S, Serra R M 2019 Phys. Rev. Lett. 123 240601Google Scholar
[142] Klatzow J, Becker J N, Ledingham P M, Weinzetl C, Kaczmarek K T, Saunders D J, Nunn J, Walmsley I A, Uzdin R, Poem E 2019 Phys. Rev. Lett. 122 110601Google Scholar
[143] Nielsen M A, Chuang I L 2011 Quantum Computation and Quantum Information (10th Ed.) (New York: Cambridge University Press) pp416–561
[144] Salles A, de Melo F, Almeida M P, Hor-Meyll M, Walborn S P, Souto Ribeiro P H, Davidovich L 2008 Phys. Rev. A 78 022322Google Scholar
[145] Passos M H M, Santos Alan C, Sarandy Marcelo S, Huguenin J A O 2019 Phys. Rev. A 100 022113Google Scholar
[146] Xiao L, Wang K K, Zhan X, Bian Z H, Kawabata K, Ueda M, Yi W, Xue P 2019 Phys. Rev. Lett. 123 230401Google Scholar
[147] Lima G, Vargas A, Neves L, Guzmán R, Saavedra C 2009 Opt. Express 17 10688Google Scholar
[148] Machado P, Matoso A A, Barros M R, Neves L, Pádua S 2019 Phys. Rev. A 99 063839Google Scholar
[149] de Assis P L, Carvalho M A D, Berruezo L P, Ferraz J, Santos I F, Sciarrino F, Pádua S 2011 Opt. Express 19 3715Google Scholar
[150] Baldijão R D, Borges G F, Marques B, Solís-Prosser M A, Neves L, Pádua S 2017 Phys. Rev. A 96 032329Google Scholar
[151] Borges G F, Baldijão R D, CondáJ G L, Cabral J S, Marques B, Terra Cunha M, Cabello A, Pádua S 2018 Phys. Rev. A 97 022301Google Scholar
[152] Cardoso A C, CondéJ G L, Marques B, Cabral J S, Pádua S 2021 Phys. Rev. A 103 013722Google Scholar
[153] Maraviglia N, Yard P, Wakefield R, Carolan J, Sparrow C, Chakhmakhchyan L, Harrold C, Hashimoto T, Matsuda N, Harter A K, Joglekar Y N, Laing A 2022 Phys. Rev. Res. 4 013051Google Scholar
[154] Schindler J, Li A, Zheng M C, Ellis F M, Kottos T 2011 Phys. Rev. A 84 040101Google Scholar
[155] Lin Z, Schindler J, Ellis F M, Kottos T 2012 Phys. Rev. A 85 050101Google Scholar
[156] 傅廷, 王宇飞, 王学友, 陈静瑄, 周旭彦, 郑婉华 2021 中国激光 48 1201005Google Scholar
Fu T, Wang Y F, Wang X Y, Chen J X, Zhou X Y, Zheng W H 2021 Chinese Journal of Lasers 48 1201005Google Scholar
[157] El-Ganainy R, Makris K G, Christodoulides D N, Musslimani Z H 2007 Opt. Lett. 32 002632Google Scholar
[158] Miri M, LiKamWa P, Christodoulides D N 2012 Opt. Lett. 37 000764Google Scholar
[159] Hodaei H, Miri M, Heinrich M, Christodoulides D N, Khajavikhan M 2014 SPIE Process. 9162 91621QGoogle Scholar
[160] Feng L, Wong Z J, Ma R M, Wang Y, Zhang X 2014 Science 346 972Google Scholar
[161] Gu Z Y, Zhang N, Lyu Q, Li M, Xiao S M, Song Q H 2016 Laser Photonics Rev. 10 588Google Scholar
[162] Miao P, Zhang Z, Sun J, Walasik W, Longhi S, Litchinitser N M, Feng L 2016 Science 353 464Google Scholar
[163] Zhang Z F, Qiao X D, Midya B, Liu K, Sun J B, Wu T W, Liu W J, Agarwal R, Jornet J M, Longhi S, Litchinitser N M, Feng L 2020 Science 368 760Google Scholar
[164] Xu H S, Jin L 2022 Phys. Rev. Res. 4 L032015Google Scholar
[165] Jin L, Song Z 2018 Phys. Rev. Lett. 121 073901Google Scholar
[166] 成恩宏, 郎利君 2022 物理学报 71 160301Google Scholar
Chen E H, Lang L J 2022 Acta Phys. Sin. 71 160301Google Scholar
计量
- 文章访问数: 7300
- PDF下载量: 355
- 被引次数: 0