Solving Differential Equations via Continuous-Variable Quantum Computers

TL;DR

This paper demonstrates how continuous-variable quantum computers can be used to solve differential equations by constructing variational circuits and using their ability to encode real numbers, showing promising simulation results.

Contribution

It introduces a method to solve differential equations on CV quantum computers using variational circuits and input/output encoding techniques, with validation through simulations.

Findings

Good convergence for linear ODEs

Effective handling of non-linear ODEs

Potential for quantum advantage in differential equation solving

Abstract

We explore how a continuous-variable (CV) quantum computer could solve a classic differential equation, making use of its innate capability to represent real numbers in qumodes. Specifically, we construct variational CV quantum circuits [Killoran et al., Phys.~Rev.~Research 1, 033063 (2019)] to approximate the solution of one-dimensional ordinary differential equations (ODEs), with input encoding based on displacement gates and output via measurement averages. Our simulations and parameter optimization using the PennyLane / Strawberry Fields framework demonstrate good convergence for both linear and non-linear ODEs.