非厄米系统的量子模拟新进展

高雪儿; 李代莉; 刘志航; 郑超

doi:10.7498/aps.71.20221825

摘要

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.

关键词:

Abstract

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.

Keywords:

作者及机构信息

北方工业大学理学院, 北京　100144

通信作者: 郑超, czheng@ncut.edu.cn

基金项目: 国家自然科学基金(批准号: 12175002, 11705004)、北京市自然科学基金(批准号: 1222020)和北京市教委优秀青年人才培育计划资助的课题

Authors and contacts

College of Science, North China Universty of Technology, Beijing 100144, China

Corresponding author: Zheng Chao, czheng@ncut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12175002, 11705004), the Natural Science Foundation of Beijing, China (Grant No. 1222020), and the Development of Talents Project for Outstanding Young Scholars of Beijing Municipal Institutions, China

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施引文献

图 1 PT对称和PPH系统的参数空间($ w, s, \theta $ 和$ v, u, \theta $, 设置$ r = 2 $)　(a) PT对称系统; (b) PPH系统^[38]

Fig. 1. Parameter spaces of PT-symmetric and P-pseudo-Hermitian systems ($ w, s, \theta $ and $ v, u, \theta $ with setting $ r = 2 $): (a) PT-symmetric systems; (b) PPH systems^[38]

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图 2 APT和APPH系统的参数空间($ w, s, \theta $和$ v, u, \theta $, 设置$ r = 2 $)　(a) APT系统; (b) APPH 系统^[38]

Fig. 2. Parameter spaces of APT-symmetric and anti-P-pseudo-Hermitian systems ($ w, s, \theta $ and $ v, u, \theta $ with setting $ r = 2 $): (a) APT-symmetric systems; (b) APPH systems^[38]

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图 3 广义PT对称二能级量子系统的量子线路^[51]

Fig. 3. Quantum circuit for a general PT-symmetric two-level system^[51]

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图 4 由辅助qutrit和辅助qudit构造广义PT对称二能级量子系统的电路图　(a)辅助qutrit; (b)辅助qudit^[51]

Fig. 4. Quantum circuit for a general PT-symmetric two-level system by ancillary qutrit or ancillary qudit: (a) Ancillary qutrit; (b) ancillary qudit^[51]

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图 5 模拟处于任意相的PT反对称二能级系统的量子线路^[55]

Fig. 5. Quantum circuit for a generalized APT-symmetric two-level system in arbitrary phase^[55]

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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]

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图 7 Qubit-qudit混合量子线路(由一个工作量子比特和四维辅助量子比特组成的混合系统)^[99]

Fig. 7. Qubit-qudit hybrid quantum circuit (The hybrid system consists of a work qubit and a four-dimensional ancillary qudit)^[99]

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图 8 三量子比特线路(由一个工作比特和两个辅助量子比特子系统构成)^[99]

Fig. 8. Three-qubit quantum circuit(consists of a work qubit and a two-qubit ancillary subsystems)^[99]

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图 9 (a) qubit-qutrit混合量子计算机的线路图; (b)三比特量子计算机的量子线路图^[101]

Fig. 9. (a) Quantum circuit for a qubit-qutrit hybrid computer; (b) quantum circuit designed for a quantum computer of three qubits^[101]

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图 10 (a) qubit-qudit混合量子计算机的线路图; (b)六维子空间中三量子比特量子计算机的线路图^[101]

Fig. 10. (a) Quantum circuit for a qubit-qudit hybrid computer; (b) quantum circuit designed for a quantum computer of three qubits using the full Hilbert space^[101]

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图 11 模拟T-APH二能级系统的三量子比特线路图^[57]

Fig. 11. Three-qubit quantum circuit to simulate a T-anti-pseudo-Hermitian two-level system^[57]

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图 12 模拟PT-APH二能级系统的三量子比特线路图^[57]

Fig. 12. Three-qubit quantum circuit to simulate a general PT-anti-pseudo-Hermitian two-level system^[57]

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图 13 由制备、演化和检测三个模块组成的实验装置^[102]

Fig. 13. Experimental configuration includes three modules: the preparation module, the evolution and the detection part^[102]

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图 14 可区分性测量的信息流实验结果^[56]

Fig. 14. Experimental results of information flow measured by distinguishability^[56]

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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]

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图 16 实验制备量子态在Bloch 球上的对应和相关经典的四面体^[133]

Fig. 16. Experimentally prepared states on the Bloch sphere and their corresponding classical tetrahedra^[133]

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图 17 LCU模拟YBE的简图^[49]

Fig. 17. Schematic illustration of the LCU simulation of the YBE by quantum optics system and a nuclear magnetic resonance quantum system^[49]

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图 18 用于准备和实现在三模平行高斯光束状态下的算符的实验装置^[152]

Fig. 18. Experimental setup used to prepare and to implement the operations on a three-path parallel Gaussian beam state^[152]

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非厄米系统的量子模拟新进展