Tensor-Programmable Quantum Circuits for Solving Differential Equations

TL;DR

This paper introduces a quantum solver for partial differential equations using tensor-programmable circuits, enabling direct implementation of complex equations with potential advantages over classical methods.

Contribution

It presents a novel quantum framework that overcomes unitary restrictions, allowing for solving a broad class of differential equations with improved capabilities.

Findings

Successfully applied to linear and nonlinear PDEs like Euler and Burgers' equations.

Demonstrated potential advantages over classical methods using turbulence data.

Utilized mid-circuit measurements and norm correction for enhanced flexibility.

Abstract

We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for linear and non-linear partial differential equations using the example of the linearized Euler equations with absorbing boundaries and the nonlinear Burgers' equation. For a turbulence data set, we demonstrate potential advantages of the quantum tensor scheme over its classical counterparts.