Solving nonlinear differential equations on noisy $156$-qubit quantum computers

TL;DR

This paper demonstrates solving nonlinear differential equations using IBM's 156-qubit quantum computers with a hybrid classical-quantum algorithm, marking progress toward practical simulations on current noisy quantum devices.

Contribution

It introduces the H-DES hybrid algorithm and applies it successfully to complex nonlinear differential equations on a 156-qubit quantum platform.

Findings

Successful solution of material deformation problem

Solution of inviscid Burgers' equation on NISQ device

Progress toward practical quantum simulations

Abstract

In this paper, we report on the resolution of nonlinear differential equations using IBM's quantum platform. More specifically, we demonstrate that the hybrid classical-quantum algorithm H-DES successfully solves a one-dimensional material deformation problem and the inviscid Burgers' equation on IBM's 156-qubit quantum computers. These results constitute a step toward performing physically relevant simulations on present-day Noisy Intermediate-Scale Quantum (NISQ) devices.