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Main Authors:	Naghmouchi, M. Yassine, Coelho, Wesley da Silva
Format:	Preprint
Published:	2024
Subjects:	Quantum Physics
Online Access:	https://arxiv.org/abs/2402.05748
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author	Naghmouchi, M. Yassine Coelho, Wesley da Silva
author_facet	Naghmouchi, M. Yassine Coelho, Wesley da Silva
contents	This paper presents a new hybrid classical-quantum approach to solve Mixed Integer Linear Programming (MILP) using neutral atom quantum computations. We apply Benders decomposition (BD) to segment MILPs into a master problem (MP) and a subproblem (SP), where the MP is addressed using a neutral-atom device, after being transformed into a Quadratic Unconstrained Binary Optimization (QUBO) model, with an automatized procedure. Our MILP to QUBO conversion tightens the upper bounds of the involved continuous variables, positively impacting the required qubit count, and the convergence of the algorithm. To solve the QUBO, we develop a heuristic for atom register embedding and apply a variational algorithm for pulse shaping. In addition, we implement a Proof of Concept (PoC) that outperforms existing solutions. We also conduct preliminary numerical results: in a series of small MILP instances our algorithm identifies over 95 percent of feasible solutions of high quality, outperforming classical BD approaches where the MP is solved using simulated annealing. To the best of our knowledge, this work is the first to utilize a neutral atom quantum processor in developing an automated, problem-agnostic framework for solving MILPs through BD.
format	Preprint
id	arxiv_https___arxiv_org_abs_2402_05748
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Mixed Integer Linear Programming Solver Using Benders Decomposition Assisted by Neutral Atom Quantum Processor Naghmouchi, M. Yassine Coelho, Wesley da Silva Quantum Physics This paper presents a new hybrid classical-quantum approach to solve Mixed Integer Linear Programming (MILP) using neutral atom quantum computations. We apply Benders decomposition (BD) to segment MILPs into a master problem (MP) and a subproblem (SP), where the MP is addressed using a neutral-atom device, after being transformed into a Quadratic Unconstrained Binary Optimization (QUBO) model, with an automatized procedure. Our MILP to QUBO conversion tightens the upper bounds of the involved continuous variables, positively impacting the required qubit count, and the convergence of the algorithm. To solve the QUBO, we develop a heuristic for atom register embedding and apply a variational algorithm for pulse shaping. In addition, we implement a Proof of Concept (PoC) that outperforms existing solutions. We also conduct preliminary numerical results: in a series of small MILP instances our algorithm identifies over 95 percent of feasible solutions of high quality, outperforming classical BD approaches where the MP is solved using simulated annealing. To the best of our knowledge, this work is the first to utilize a neutral atom quantum processor in developing an automated, problem-agnostic framework for solving MILPs through BD.
title	Mixed Integer Linear Programming Solver Using Benders Decomposition Assisted by Neutral Atom Quantum Processor
topic	Quantum Physics
url	https://arxiv.org/abs/2402.05748

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