# Variational quantum simulation of general processes

## TL;DR

This paper develops a unified variational quantum algorithm framework for simulating general quantum processes, including non-Hermitian evolution, linear algebra problems, and open system dynamics, with numerical validation on a six-qubit model.

## Contribution

It introduces a comprehensive variational quantum simulation approach for diverse quantum processes, extending existing methods to non-Hermitian and open systems.

## Key findings

- Unified framework for generalized time evolution.
- Application to linear algebra problems via quantum simulation.
- Numerical validation on a six-qubit dissipative model.

## 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---generalised time evolution with a non-Hermitian Hamiltonian, linear algebra problems, and open quantum system dynamics. The algorithm for generalised 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 generalised 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 Schr\"odinger equation, which consists of dissipative evolution and stochastic jump processes. We numerically test the algorithm with a six-qubit 2D transverse field Ising model under dissipation.

---
Source: https://tomesphere.com/paper/1812.08778