Variational quantum simulation of the quantum critical regime

doi:10.1088/1674-1056/accb43

中国物理B ›› 2023, Vol. 32 ›› Issue (8): 80305-080305.doi: 10.1088/1674-1056/accb43

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

收稿日期:2023-01-11 修回日期:2023-04-06 接受日期:2023-04-07 发布日期:2023-07-26
通讯作者: Dan-Bo Zhang E-mail:dbzhang@m.scnu.edu.cn
基金资助:
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).

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

Received:2023-01-11 Revised:2023-04-06 Accepted:2023-04-07 Published:2023-07-26
Contact: Dan-Bo Zhang E-mail:dbzhang@m.scnu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: quantum algorithm, quantum simulation, quantum critical point

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.

Key words: quantum algorithm, quantum simulation, quantum critical point

中图分类号: (Quantum algorithms, protocols, and simulations)

03.67.Ac

64.60.F- (Equilibrium properties near critical points, critical exponents)

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[J]. 中国物理B, 2023, 32(8): 80305-080305.

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[J]. Chin. Phys. B, 2023, 32(8): 80305-080305.

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Variational quantum simulation of the quantum critical regime

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