|
|
Variational quantum simulation of the quantum critical regime |
Zhi-Quan Shi(石志全)1, Xu-Dan Xie(谢旭丹)1, and Dan-Bo Zhang(张旦波)1,2,† |
1. Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China; 2. Guangdong--Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China |
|
|
Abstract The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures. While it is of great physical interest, simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity. Herein, we propose a variational approach, which minimizes the variational free energy, to simulate and locate the quantum critical regime on a quantum computer. The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state, in which the entropy can be analytically obtained from the initial state, and thus the free energy can be accessed conveniently. With numeral simulation, using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line. Moreover, the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states. Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.
|
Received: 11 January 2023
Revised: 06 April 2023
Accepted manuscript online: 07 April 2023
|
PACS:
|
03.67.Ac
|
(Quantum algorithms, protocols, and simulations)
|
|
64.60.F-
|
(Equilibrium properties near critical points, critical exponents)
|
|
Fund: This work was supported by the National Natural Science Foundation of China (Grant No.12005065) and the Guangdong Basic and Applied Basic Research Fund (Grant No.2021A1515010317). |
Corresponding Authors:
Dan-Bo Zhang
E-mail: dbzhang@m.scnu.edu.cn
|
Cite this article:
Zhi-Quan Shi(石志全), Xu-Dan Xie(谢旭丹), and Dan-Bo Zhang(张旦波) Variational quantum simulation of the quantum critical regime 2023 Chin. Phys. B 32 080305
|
[1] Sachdev S 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press) [2] Lee P A, Nagaosa N and Wen X G 2006 Rev. Mod. Phys. 78 17 [3] Meyer-Ortmanns H 1996 Rev. Mod. Phys. 68 473 [4] Stephanov M, Rajagopal K and Shuryak E 1998 Phys. Rev. Lett. 81 4816 [5] Troyer M and Wiese U J 2005 Phys. Rev. Lett 94 170201 [6] Barends R, Lamata L, Kelly J, et al. 2015 Nat. Commun. 6 7654 [7] Bernien H, Schwartz S, Keesling A, Levine H, Omran A, Pichler H, Choi S, Zibrov A S, Endres M, Greiner M, Vuletić V and Lukin M D 2017 Nature 551 579 [8] Kandala A, Mezzacapo A, Temme K, Takita M, Brink M, Chow J M and Gambetta J M 2017 Nature 549 242 [9] Zhang J, Pagano G, Hess P W, Kyprianidis A, Becker P, Kaplan H, Gorshkov A V, Gong Z X and Monroe C 2017 Nature 551 601 [10] Yang B, Sun H, Ott R, Wang H Y, Zache T V, Halimeh J C, Yuan Z S, Hauke P and Pan J W 2020 Nature 587 392 [11] Terhal B M and DiVincenzo D P 2000 Phys. Rev. A 61 022301 [12] Poulin D and Wocjan P 2009 Phys. Rev. Lett. 103 220502 [13] Temme K, Osborne T J, Vollbrecht K G, Poulin D and Verstraete F 2011 Nature 471 87 [14] Riera A, Gogolin C and Eisert J 2012 Phys. Rev. Lett. 108 080402 [15] Wu J and Hsieh T H 2019 Phys. Rev. Lett. 123 220502 [16] Verdon G, Marks J, Nanda S, Leichenauer S and Hidary J 2019 arXiv:1910.02071 [quant-ph] [17] Liu J G, Mao L, Zhang P and Wang L 2021 Mach. Learn.: Sci. Technol. 2 025011 [18] Chowdhury A N, Low G H and Wiebe N 2020 arXiv:2002.00055 [quant-ph] [19] Wang Y, Li G and Wang X 2021 Phys. Rev. Appl. 16 054035 [20] Zhu D, Johri S, Linke N M, Landsman K A, Alderete C H, Nguyen N H, Matsuura A Y, Hsieh T H and Monroe C 2020 Proc. Natl. Acad. Sci. USA 117 25402 [21] Zhang D B, Zhang G Q, Xue Z Y, Zhu S L and Wang Z 2021 Phys. Rev. Lett. 127 020502 [22] Xie X D, Guo X, Xing H, Xue Z Y, Zhang D B and Zhu S L (QuNu Collaboration) 2022 Phys. Rev. D 106 054509 [23] McArdle S, Jones T, Endo S, Li Y, Benjamin S C and Yuan X 2019 npj Quantum Information 5 75 [24] Preskill J 2018 Quantum 2 79 [25] Lau H K, Pooser R, Siopsis G and Weedbrook C 2017 Phys. Rev. Lett. 118 080501 [26] Zhang D B, Zhu S L and Wang Z D 2020 Phys. Rev. Lett. 124 010506 [27] Cerezo M, Arrasmith A, Babbush R, Benjamin S C, Endo S, Fujii K, McClean J R, Mitarai K, Yuan X, Cincio L and Coles P J 2021 Nat. Rev. Phys. 3 625 [28] McArdle S, Endo S, Aspuru-Guzik A, Benjamin S C and Yuan X 2020 Rev. Mod. Phys. 92 015003 [29] Huang H L, Xu X Y, Guo C, Tian G, Wei S J, Sun X, Bao W S and Long G L 2022 arXiv:2211.08737 [quant-ph] [30] Kitaev A Y 2001 Phys. Usp. 44 131 [31] Kardar M 2007 Statistical Physics of Particles (Cambridge: Cambridge University Press) [32] Cuccoli A, Taiti A, Vaia R and Verrucchi P 2007 Phys. Rev. B 76 064405 [33] Amico L and Patané D 2007 Europhys. Lett. 77 17001 [34] Frérot I and Roscilde T 2019 Nat. Commun. 10 577 [35] Kliesch M, Gogolin C, Kastoryano M, Riera A and Eisert J 2014 Phys. Rev. X 4 031019 [36] Kuwahara T, Alhambra A M and Anshu A 2021 Phys. Rev. X 11 011047 [37] Ho W W and Hsieh T H 2019 SciPost Phys. 6 029 [38] Klich I, Refael G and Silva A 2006 Phys. Rev. A 74 032306 [39] Islam R, Ma R, Preiss P M, Eric Tai M, Lukin A, Rispoli M and Greiner M 2015 Nature 528 77 [40] Brydges T, Elben A, Jurcevic P, Vermersch B, Maier C, Lanyon B P, Zoller P, Blatt R and Roos C F 2019 Science 364 260 [41] Audenaert K M 2007 J. Phys. A: Math. Theor. 40 8127 [42] Acharya J, Issa I, Shende N V and Wagner A B 2020 IEEE J. Sel. Areas Inf. Theory 1 454 [43] Martyn J and Swingle B 2019 Phys. Rev. A 100 032107 [44] Liu J G, Mao L, Zhang P and Wang L 2021 Mach. Learn.: Sci. Technol. 2 025011 [45] Chen B L and Zhang D B 2023 Chin. Phys. Lett. 40 010303 [46] Nielsen M A and Chuang I 2010 Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge: Cambridge University Press) [47] Cross A 2018 The IBM Q experience and QISKIT open-source quantum computing software. In: APS March Meeting Abstracts Vol. 2018 p. L58-003 [48] Wiersema R, Zhou C, de Sereville Y, Carrasquilla J F, Kim Y B and Yuen H 2020 PRX Quantum 1 020319 [49] Hadfield S, Wang Z, O'Gorman B, Rieffel E G, Venturelli D and Biswas R 2017 Algorithms 12 34 [50] Pedernales J S, Di Candia R, Egusquiza I L, Casanova J and Solano E 2014 Phys. Rev. Lett. 113 020505 [51] Li T, Guo X, Lai W K, Liu X, Wang E, Xing H, Zhang D B and Zhu S L (QuNu Collaboration) 2022 Phys. Rev. D 105 L111502 [52] Fisher M E and Barber M N 1972 Phys. Rev. Lett. 28 1516 [53] Johansson J R, Nation P D and Nori F 2012 Comput. Phys. Commun. 183 1760 [54] Zhang D B and Yin T 2020 Phys. Rev. A 101 032311 [55] Yuan Z H, Yin T and Zhang D B 2021 Phys. Rev. A 103 012413 |
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|