Quantum Model-Discovery

TL;DR

This paper introduces Quantum Model Discovery (QMoD), a method leveraging near-term quantum computers and differentiable quantum circuits to identify and infer differential equations from data, bridging classical and quantum machine learning.

Contribution

It extends quantum algorithms for PDEs to the discovery of differential equations from data using differentiable quantum circuits, enabling new scientific machine learning applications.

Findings

Successful parameter inference on differential equations

Equation discovery demonstrated on PDEs and ODEs

Promising approach for quantum-assisted scientific modeling

Abstract

Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization. Many problems appearing in science and engineering can be rewritten as a set of differential equations. Quantum algorithms for solving differential equations have shown a provable advantage in the fault-tolerant quantum computing regime, where deep and wide quantum circuits can be used to solve large linear systems like partial differential equations (PDEs) efficiently. Recently, variational approaches to solving non-linear PDEs also with near-term quantum devices were proposed. One of the most promising general approaches is based on recent developments in the field of scientific machine learning for solving PDEs. We extend the applicability of near-term quantum computers to more general scientific machine learning tasks, including the discovery of differential equations from a dataset of measurements. We use differentiable quantum circuits (DQCs) to solve equations parameterized by a library of operators, and perform regression on a combination of data and equations. Our results show a promising path to Quantum Model Discovery (QMoD), on the interface between classical and quantum machine learning approaches. We demonstrate successful parameter inference and equation discovery using QMoD on different systems including a second-order, ordinary differential equation and a non-linear, partial differential equation.