Quantum simulation of τ-anti-pseudo-Hermitian two-level systems

doi:10.1088/1674-1056/ac8738

Abstract Different from the Hermitian case, non-Hermitian (NH) systems have novel properties and strongly relate to open and dissipative quantum systems. In this work, we investigate how to simulate τ-anti-pseudo-Hermitian systems in a Hermitian quantum device using linear combinations of unitaries and duality quantum algorithm. Specifying the τ to time-reversal (T) and parity-time-reversal (PT) operators, we construct the two NH two-level systems, design quantum circuits including three qubits, and decide the quantum gates explicitly in detail. We also calculate the success probabilities of the simulation. Experimental implementation can be expected in small quantum simulator.

Keywords: quantum simulation linear combination of unitaries non-Hermitian anti-pseudo-Hermitian

Received: 05 June 2022
Revised: 10 July 2022
Accepted manuscript online:

PACS:	03.67.Ac	(Quantum algorithms, protocols, and simulations)
	03.65.Yz	(Decoherence; open systems; quantum statistical methods)
	03.65.Aa	(Quantum systems with finite Hilbert space)
	11.30.Er	(Charge conjugation, parity, time reversal, and other discrete symmetries)

Fund: This work was funded by the National Natural Science Foundation of China (Grant No. 12175002), Beijing Natural Science Foundation (Grant No. 1222020), and NCUT Talents Project and Special Fund for C.Z.

Corresponding Authors: Chao Zheng
E-mail: czheng@ncut.edu.cn

Cite this article:

Chao Zheng(郑超) Quantum simulation of τ-anti-pseudo-Hermitian two-level systems 2022 Chin. Phys. B 31 100301

[1] Breuer H P and Petruccione F 2002 The Theory of Open Quantum Systems (10th anniversary edition) (Oxford: Oxford University Press)
[2] Barreiro J T, Müller M, Schindler P, et al. 2011 Nature 470 486
[3] Hu Z, Xia R and Kais S 2020 Sci. Rep. 10 3301
[4] Del Re L, Rost B, Kemper A F and Freericks J K 2020 Phys. Rev. B 102 125112
[5] Viyuela O, Rivas A, Gasparinetti S, Wallraff A, Filipp S and MartinDelgado M A 2018 npj Quantum Inf. 4 10
[6] Zheng C 2021 Sci. Rep. 11 3960
[7] Schlimgen A W, Head-Marsden K, Sager L M, Narang P and Mazziotti D A 2021 Phys. Rev. Lett. 127 270503
[8] Del Re L, Rost B, Foss-Feig M, Kemper A F and Freericks J K 2022 arXiv 2204.12400
[9] Ding P Z and Yi W 2022 Chin. Phys. B 31 010309
[10] Lee T D and Wick G C 1969 Nucl. Phys. B 9 209
[11] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[12] Bender C M, Boettcher S and Meisinger P N 1999 J. Math. Phys. 40 2201
[13] Bender C M, Brody D C and Jones H F 2002 Phys. Rev. Lett. 89 270401
[14] Bender C M, Brody D C and Jones H F 2003 Am. J. Phys. 71 1095
[15] Bender C M 2015 J. Phys.: Conf. Ser. 631 012002
[16] Zhang S, Jin L and Song Z 2022 Chin. Phys. B 31 010312
[17] Hu Z, Jin L, Zeng Z Y, Tang J and Luo X B 2022 Acta Phys. Sin. 71 074207 (in Chinese)
[18] Mostafazadeh A 2002 J. Math. Phys. 43 205
[19] Mostafazadeh A 2002 J. Math. Phys. 43 2814
[20] Konotop V V, Yang Z and Zezyulin D A 2016 Rev. Mod. Phys. 88 035002
[21] Mostafazadeh A 2002 J. Math. Phys. 43 3944
[22] Mostafazadeh A 2003 J. Math. Phys. 44 974
[23] Zeng C, Guo Z, Zhu K, Fan C, Li G, Jiang J, Li Y, Jiang H, Yang Y, Sun Y and Chen H 2022 Chin. Phys. B 31 010307
[24] Zhang D J, Wang Q H and Gong J 2021 Chin. Phys. B 30 100307
[25] Zhou L and Han W 2021 Chin. Phys. B 30 100308
[26] Wang Z, Xiang Z, Liu T, Song X, Song P, Guo X, Su L, Zhang H, Du Y and Zheng D 2021 Chin. Phys. B 30 100309
[27] Yang X, Cao Y and Zhai Y 2022 Chin. Phys. B 31 010308
[28] Liang H Q and Li L 2022 Chin. Phys. B 31 010310
[29] Xue P 2022 Chin. Phys. B 31 010311
[30] Guo C X and Chen S 2022 Chin. Phys. B 31 010313
[31] Zhang H, Peng M, Xu X W and Jing H 2022 Chin. Phys. B 31 014215
[32] Cheng S and Gao X 2022 Chin. Phys. B 31 017401
[33] Jiang H and Lee C H 2022 Chin. Phys. B 31 050307
[34] Zheng C, Hao L and Long G L 2013 Phil. Trans. R. Soc. A 371 20120053
[35] Peng B, Özdemir Ş K, Lei F, Monifi F, Gianfreda M, Long G L, Fan S, Nori F, Bender C M and Yang L 2014 Nat. Phys. 10 394
[36] Xu W L, Liu X F, Sun Y, Gao Y P, Wang T J and Wang C 2020 Phys. Rev. E 101 012205
[37] Gao W C, Zheng C, Liu L, Wang T J and Wang C 2021 Opt. Exp. 29 517
[38] Lu B, Liu X F, Sun Y, Gao Y P, Cao C, Wang T J and Wang C 2019 Opt. Express 27 22237
[39] Wang K, Gao Y P, Jiao R and Wang C 2022 Front. Phys. 17 42201
[40] Zheng C, Tian J, Li D, Wen J, Wei S and Li Y S 2020 Entropy 22 812
[41] Solombrino L 2002 J. Math. Phys. 43 5439
[42] Nixon S and Yang J 2016 Phys. Rev. A 93 031802(R)
[43] Mostafazadeh A 2020 Entropy 22 471
[44] Pinske J, Teuber L and Scheel S 2019 Phys. Rev. A 100 042316
[45] Chu Y, Liu Y, Liu H and Cai J 2020 Phys. Rev. Lett. 124 020501
[46] Jin L 2022 Chin. Phys. Lett. 39 037302
[47] Ge L and Tureci H E 2013 Phys. Rev. A 88 053810
[48] Hang C, Huang G and Konotop V V 2013 Phys. Rev. Lett. 110 083604
[49] Antonosyan D A, Solntsev A S and Sukhorukov A A 2015 Opt. Lett. 40 4575
[50] Wu J H, Artoni M and La Rocca G C 2015 Phys. Rev. A 91 033811
[51] Peng P, Cao W, Shen C, et al. 2016 Nat. Phys. 12 1139
[52] Yang F, Liu Y C and You L 2017 Phys. Rev. A 96 053845
[53] Choi Y, Hahn C, Yoon J W, et al. 2018 Nat. Comm. 9 2182
[54] Konotop V V and Zezyulin D A 2018 Phys. Rev. Lett. 120 123902
[55] Chuang Y L, Ziauddin and Lee R K 2018 Opt. Express 26 21969
[56] Li Y, Peng Y G, Han L, et al. 2019 Science 364 170
[57] Zheng C 2019 Europhys. Lett. 126 30005
[58] Wen J, Qin G, Zheng C, Wei S, Kong X, Xin T and Long G 2020 npj Quantum Inf. 6 28
[59] Feynman R 1982 Int. J. Theor. Phys. 21 467
[60] Greiner M, Mandel O, Esslinger T, et al. 2002 Nature 415 39
[61] Leibfried D, DeMarco B, Wineland D J, et al. 2002 Phys. Rev. Lett. 89 247901
[62] Friedenauer A, Schmitz H, Schatz T, et al. 2008 Nat. Phys. 4 757
[63] Kim K, Duan L M, Monroe C, et al. 2010 Nature 465 590
[64] Lanyon B P, Aspuru-Guzik A and White A G 2010 Nat. Chem. 2 106
[65] Gerritsma R, Kirchmair G, Zähringer F, et al. 2010 Nature 463 68
[66] Zheng C, Song S Y, Li J L and Long G L 2013 J. Opt. Soc. Am. B 30 1688
[67] Georgescu I M, Ashhab S and Nori F 2014 Rev. Mod. Phys. 86 153
[68] Setia K, Bravyi S, Mezzacapo A and Whitfield J D 2019 Phys. Rev. Research 1 033033
[69] Aspuru-Guzik A and Walther P 2012 Nat. Phys. 8 285
[70] Pearson J, Feng G R, Zheng C and Long G L 2016 Sci. China Phys. Mech. Astron. 59 120312
[71] Sheng Y B and Zhou L 2017 Sci. Bull. 62 1025
[72] Zheng C 2018 Europhys. Lett. 123 40002
[73] Wen J, Zheng C, Kong X, Wei S, Xin T and Long G 2019 Phys. Rev. A 99 062122
[74] Wen J, Zheng C, Ye Z, Xin T and Long G L 2021 Phys. Rev. Research 3 013256
[75] Li X G, Zheng C, Gao J C and Long G L 2022 Phys. Rev. A 105 032405
[76] Zheng C 2021 Europhys. Lett. 136 30002
[77] Zheng C and Wei S J 2018 Int. J. Theor. Phys. 57 2203
[78] Wang H, Wei S, Zheng C, Kong X, Wen J, Nie X, Li J, Lu D and Xin T 2020 Phys. Rev. A 102 012610
[79] Zheng C and Li D 2022 Sci. Rep. 12 2824
[80] Long G L and Li C Y 2006 Commun. Theor. Phys. 45 825 (It was submitted in an abstract to SPIE conference ‘Fluctuations and Noise 2003’: Abstract (5111-53) in 2002)
[81] Streater R F and Wightman A S 1964 PCT, spin, statistics and all that (New York: Benjamin press).
[82] Onsager L 1931 Phys. Rev. 37 405
[83] Lee T D and Yang C N 1956 Phys. Rev. 104 254
[84] Sigwarth O and Miniatura C 2022 AAPPS Bull. 32 23
[85] Wu C S, Ambler E, Hayward R W, Hoppes D D and Hudson R P 1957 Phys. Rev. 105 1413
[86] Kato T 1966 Perturbation theory for linear operators (Berlin: Springer)
[87] Gao Y P, Sun Y, Liu X F, Wang T J and Wang C 2019 IEEE Access 7 107874
[88] Long G L and Liu Y 2008 Front. Comput. Sci. 2 167
[89] Long G L, Liu Y and Wang C 2009 Commun. Theor. Phys. 51 65
[90] Long G L 2011 Int. J. Theor. Phys. 50 1305
[91] Cui J, Zhou T and Long G L 2012 Quantum Inf. Process. 11 317
[92] Qiang X G, Zhou X Q, Wang J W, et al. 2018 Nat. Photon. 12 534
[93] Wei S J, Li H and Long G L 2020 Research 2020 1486935
[94] Shao C P, Li Y and Li H B 2019 J. Sys. Sci. Complex. 32 375
[95] Neeley M, Ansmann M, Bialczak R C, et al. 2009 Science 325 722
[96] Cao Y, Peng S G, Zheng C and Long G L 2011 Comm. Theor. 55 790
[97] Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (10th Anniversary Edition) (Cambridge: Cambridge University Press) pp. 221–225
[98] Fan C R, Lu B, Feng X T, Gao W C and Wang C 2021 Quantum Engineering 3 e67
[99] Cory D G, Price M D and Havel T F 2008 Physica D 120 82
[100] Hu S W, Xue K and Ge M L 2008 Phys. Rev. A 78 022319
[101] Knill E, Laflamme R and Milburn G A 2001 Nature 409 46
[102] Cerf N J, Adami C and Kwiat P G 1998 Phys. Rev. A 57 R1477(R)

[1]	Fast population transfer with a superconducting qutrit via non-Hermitian shortcut to adiabaticity Xin-Ping Dong(董新平), Zhi-Bo Feng(冯志波), Xiao-Jing Lu(路晓静), Ming Li(李明), and Zheng-Yin Zhao(赵正印). Chin. Phys. B, 2023, 32(3): 034201.
[2]	Observation of size-dependent boundary effects in non-Hermitian electric circuits Luhong Su(苏鹭红), Cui-Xian Guo(郭翠仙), Yongliang Wang(王永良), Li Li(李力), Xinhui Ruan(阮馨慧), Yanjing Du(杜燕京), Shu Chen(陈澍), and Dongning Zheng(郑东宁). Chin. Phys. B, 2023, 32(3): 038401.
[3]	Hall conductance of a non-Hermitian two-band system with k-dependent decay rates Junjie Wang(王俊杰), Fude Li(李福德), and Xuexi Yi(衣学喜). Chin. Phys. B, 2023, 32(2): 020305.
[4]	Mobility edges generated by the non-Hermitian flatband lattice Tong Liu(刘通) and Shujie Cheng(成书杰). Chin. Phys. B, 2023, 32(2): 027102.
[5]	Variational quantum simulation of thermal statistical states on a superconducting quantum processer Xue-Yi Guo(郭学仪), Shang-Shu Li(李尚书), Xiao Xiao(效骁), Zhong-Cheng Xiang(相忠诚), Zi-Yong Ge(葛自勇), He-Kang Li(李贺康), Peng-Tao Song(宋鹏涛), Yi Peng(彭益), Zhan Wang(王战), Kai Xu(许凯), Pan Zhang(张潘), Lei Wang(王磊), Dong-Ning Zheng(郑东宁), and Heng Fan(范桁). Chin. Phys. B, 2023, 32(1): 010307.
[6]	Real non-Hermitian energy spectra without any symmetry Boxue Zhang(张博学), Qingya Li(李青铔), Xiao Zhang(张笑), and Ching Hua Lee(李庆华). Chin. Phys. B, 2022, 31(7): 070308.
[7]	Filling up complex spectral regions through non-Hermitian disordered chains Hui Jiang and Ching Hua Lee. Chin. Phys. B, 2022, 31(5): 050307.
[8]	Measuring Loschmidt echo via Floquet engineering in superconducting circuits Shou-Kuan Zhao(赵寿宽), Zi-Yong Ge(葛自勇), Zhong-Cheng Xiang(相忠诚), Guang-Ming Xue(薛光明), Hai-Sheng Yan(严海生), Zi-Ting Wang(王子婷), Zhan Wang(王战), Hui-Kai Xu(徐晖凯), Fei-Fan Su(宿非凡), Zhao-Hua Yang(杨钊华), He Zhang(张贺), Yu-Ran Zhang(张煜然), Xue-Yi Guo(郭学仪), Kai Xu(许凯), Ye Tian(田野), Hai-Feng Yu(于海峰), Dong-Ning Zheng(郑东宁), Heng Fan(范桁), and Shi-Ping Zhao(赵士平). Chin. Phys. B, 2022, 31(3): 030307.
[9]	Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics Zi-Yong Ge(葛自勇), Rui-Zhen Huang(黄瑞珍), Zi-Yang Meng(孟子杨), and Heng Fan(范桁). Chin. Phys. B, 2022, 31(2): 020304.
[10]	Quantum simulation and quantum computation of noisy-intermediate scale Kai Xu(许凯), and Heng Fan(范桁). Chin. Phys. B, 2022, 31(10): 100304.
[11]	Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence Xiaosen Yang(杨孝森), Yang Cao(曹阳), and Yunjia Zhai(翟云佳). Chin. Phys. B, 2022, 31(1): 010308.
[12]	Two-body exceptional points in open dissipative systems Peize Ding(丁霈泽) and Wei Yi(易为). Chin. Phys. B, 2022, 31(1): 010309.
[13]	Topological properties of non-Hermitian Creutz ladders Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎). Chin. Phys. B, 2022, 31(1): 010310.
[14]	Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions Cui-Xian Guo(郭翠仙) and Shu Chen(陈澍). Chin. Phys. B, 2022, 31(1): 010313.
[15]	Efficient and stable wireless power transfer based on the non-Hermitian physics Chao Zeng(曾超), Zhiwei Guo(郭志伟), Kejia Zhu(祝可嘉), Caifu Fan(范才富), Guo Li(李果), Jun Jiang(江俊), Yunhui Li(李云辉), Haitao Jiang(江海涛), Yaping Yang(羊亚平), Yong Sun(孙勇), and Hong Chen(陈鸿). Chin. Phys. B, 2022, 31(1): 010307.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Quantum simulation of τ-anti-pseudo-Hermitian two-level systems

Cite this article:

Online attention