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Variational Quantum Simulation of General Processes.

Suguru Endo1,2, Jinzhao Sun3, Ying Li4

  • 1Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom.

Physical Review Letters
|July 18, 2020
PubMed
Summary
This summary is machine-generated.

This study explores variational quantum simulation for diverse quantum tasks, including non-Hermitian dynamics, linear algebra, and open quantum systems. The findings unify simulation frameworks and demonstrate practical applications for quantum computing.

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Area of Science:

  • Quantum Computing
  • Quantum Simulation
  • Computational Physics

Background:

  • Variational quantum algorithms (VQAs) are promising for simulating closed many-body quantum systems.
  • Current VQAs primarily focus on static properties and dynamics of closed systems.
  • There is a need for VQAs capable of handling more complex quantum tasks.

Purpose of the Study:

  • To investigate variational quantum simulation for generalized time evolution with non-Hermitian Hamiltonians.
  • To explore variational approaches for solving linear algebra problems using quantum simulation.
  • To develop and test variational methods for simulating open quantum system dynamics.

Main Methods:

  • Developed a unified framework for generalized time evolution in variational quantum simulation.
  • Applied the generalized time evolution to solve linear systems of equations and matrix-vector multiplication.
  • Proposed a combined variational real and imaginary time evolution for algebraic problems.
  • Implemented variational quantum simulation for the stochastic Schrödinger equation, including dissipative and jump processes.

Main Results:

  • The generalized time evolution algorithm provides a unified approach for variational quantum simulation.
  • Linear algebra problems were successfully mapped to generalized time evolution tasks.
  • A novel variational method combining real and imaginary time evolution was proposed for algebraic problems.
  • Variational simulation of open quantum systems was demonstrated, tested on a 6-qubit 2D transverse field Ising model under dissipation.

Conclusions:

  • Variational quantum simulation can be extended to address a broader range of quantum problems beyond closed systems.
  • The proposed methods offer efficient quantum computational approaches for linear algebra and open quantum dynamics.
  • This work lays the groundwork for more versatile and powerful variational quantum algorithms.