• Open Access

Variational Quantum Simulation of General Processes

Suguru Endo, Jinzhao Sun, Ying Li, Simon C. Benjamin, and Xiao Yuan
Phys. Rev. Lett. 125, 010501 – Published 29 June 2020
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Abstract

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.

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  • Received 14 June 2019
  • Revised 11 May 2020
  • Accepted 2 June 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.010501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Suguru Endo1,4,*, Jinzhao Sun2, Ying Li3, Simon C. Benjamin1, and Xiao Yuan1,†

  • 1Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
  • 2Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
  • 3Graduate School of China Academy of Engineering Physics, Beijing 100193, China
  • 4NTT Secure Platform Laboratories, NTT Corporation, Musashino 180-8585, Japan

  • *suguru.endou.uc@hco.ntt.co.jp
  • xiao.yuan.ph@gmail.com

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Issue

Vol. 125, Iss. 1 — 3 July 2020

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