Mixed-Integer Programming Using a Bosonic Quantum Computer

TL;DR

This paper introduces a quantum computing approach using bosonic qumodes to solve mixed-integer programming problems by translating them into ground-state preparation tasks, demonstrated through numerical simulations.

Contribution

It presents a novel method for solving mixed-integer programming problems on bosonic quantum computers, expanding quantum optimization techniques.

Findings

Successfully simulated solving small non-convex optimization problems

Demonstrated adiabatic evolution from initial to final Hamiltonian

Applied to integer, continuous, and mixed-integer programming

Abstract

We propose a scheme for solving mixed-integer programming problems in which the optimization problem is translated to a ground-state preparation problem on a set of bosonic quantum field modes (qumodes). We perform numerical demonstrations by simulating a circuit-based optical quantum computer with each individual qumode prepared in a Gaussian state. We simulate an adiabatic evolution from an initial mixing Hamiltonian, written in terms of the momentum operators of the qumodes, to a final Hamiltonian which is a polynomial of the position and boson number operators. In these demonstrations, we solve a variety of small non-convex optimization problems in integer programming, continuous non-convex optimization, and mixed-integer programming.