Experimental differentiation and extremization with analog quantum circuits

TL;DR

This paper demonstrates the first experimental use of differentiable quantum circuits and quantum extremal learning on a commercial analog quantum computer, showcasing their potential for solving and optimizing differential equations in scientific computing.

Contribution

It provides the first experimental demonstration of DQC and QEL on an analog quantum computer, challenging the assumption that digital hardware is necessary for such tasks.

Findings

Successful implementation of DQC and QEL on analog hardware

Demonstration of solving differential equations with quantum circuits

Challenging the need for digital quantum computers for these methods

Abstract

Solving and optimizing differential equations (DEs) is ubiquitous in both engineering and fundamental science. The promise of quantum architectures to accelerate scientific computing thus naturally involved interest towards how efficiently quantum algorithms can solve DEs. Differentiable quantum circuits (DQC) offer a viable route to compute DE solutions using a variational approach amenable to existing quantum computers, by producing a machine-learnable surrogate of the solution. Quantum extremal learning (QEL) complements such approach by finding extreme points in the output of learnable models of unknown (implicit) functions, offering a powerful tool to bypass a full DE solution, in cases where the crux consists in retrieving solution extrema. In this work, we provide the results from the first experimental demonstration of both DQC and QEL, displaying their performance on a synthetic usecase. Whilst both DQC and QEL are expected to require digital quantum hardware, we successfully challenge this assumption by running a closed-loop instance on a commercial analog quantum computer, based upon neutral atom technology.