A hybrid quantum solver for the Lorenz system

TL;DR

This paper introduces a hybrid classical-quantum approach using the Variational Quantum Linear Solver to efficiently solve the Lorenz system, demonstrating comparable accuracy to classical methods and potential for broader nonlinear differential equations.

Contribution

The paper presents a novel hybrid quantum-classical method employing VQLS for solving nonlinear differential equations like the Lorenz system.

Findings

VQLS effectively computes solutions similar to classical methods.

The hybrid approach is extendable to other nonlinear differential equations.

Numerical results validate the method's accuracy and efficiency.

Abstract

We develop a hybrid classical-quantum method for solving the Lorenz system. We use the forward Euler method to discretize the system in time, transforming it into a system of equations. This set of equations is solved using the Variational Quantum Linear Solver (VQLS) algorithm. We present numerical results comparing the hybrid method with the classical approach for solving the Lorenz system. The simulation results demonstrate that the VQLS method can effectively compute solutions comparable to classical methods. The method is easily extended to solving similar nonlinear differential equations.