Endo Suguru, Sun Jinzhao, Li Ying, Benjamin Simon C, Yuan Xiao
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom.
NTT Secure Platform Laboratories, NTT Corporation, Musashino 180-8585, Japan.
Phys Rev Lett. 2020 Jul 3;125(1):010501. doi: 10.1103/PhysRevLett.125.010501.
Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks-generalized time evolution with a non-Hermitian Hamiltonian, linear algebra problems, and open quantum system dynamics. The algorithm for generalized time evolution provides a unified framework for variational quantum simulation. In particular, we show its application in solving linear systems of equations and matrix-vector multiplications by converting these algebraic problems into generalized time evolution. Meanwhile, assuming a tensor product structure of the matrices, we also propose another variational approach for these two tasks by combining variational real and imaginary time evolution. Finally, we introduce variational quantum simulation for open system dynamics. We variationally implement the stochastic Schrödinger equation, which consists of dissipative evolution and stochastic jump processes. We numerically test the algorithm with a 6-qubit 2D transverse field Ising model under dissipation.
变分量子算法已被提出用于解决封闭多体量子系统的静态和动态问题。在此，我们研究三种一般类型任务的变分量子模拟——具有非厄米哈密顿量的广义时间演化、线性代数问题以及开放量子系统动力学。广义时间演化算法为变分量子模拟提供了一个统一框架。特别地，我们通过将这些代数问题转化为广义时间演化，展示了其在求解线性方程组和矩阵 - 向量乘法中的应用。同时，假设矩阵具有张量积结构，我们还通过结合变分实时间演化和虚时间演化，为这两个任务提出了另一种变分方法。最后，我们介绍开放系统动力学的变分量子模拟。我们通过变分实现由耗散演化和随机跳跃过程组成的随机薛定谔方程。我们在耗散情况下用一个6量子比特的二维横向场伊辛模型对该算法进行了数值测试。
