非厄米系统的量子模拟新进展

Recent progress of quantum simulation of non-Hermitian systems

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.