Variational Quantum Simulation of General Processes.,Physical Review Letters

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Variational Quantum Simulation of General Processes.
Physical Review Letters ( IF 8.1 ) Pub Date : 2020-06-29 , DOI: 10.1103/physrevlett.125.010501
Suguru Endo _{1,

2} , Jinzhao Sun ₃ , Ying Li ₄ , Simon C Benjamin ₁ , Xiao Yuan ₁

Affiliation

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.

中文翻译：

一般过程的变分量子模拟。

已经提出了变分量子算法来解决封闭多体量子系统的静态和动态问题。在这里，我们研究三种常见任务的变分量子模拟-具有非Hermitian哈密顿量的广义时间演化，线性代数问题和开放量子系统动力学。广义时间演化算法为变分量子仿真提供了统一的框架。特别是，通过将这些代数问题转换为广义时间演化，我们展示了其在求解方程式和矩阵向量乘法的线性系统中的应用。同时，假设矩阵的张量积结构，我们还通过结合变化的实部和虚部时间演化来针对这两个任务提出另一种变化方法。最后，我们介绍了用于开放系统动力学的变分量子模拟。我们变分地执行随机Schrödinger方程，该方程由耗散演化和随机跳跃过程组成。我们在耗散条件下使用6比特2D横向场Ising模型对算法进行了数值测试。

更新日期：2020-06-29

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