Optimization of Quantum Systems Emulation via a Variant of the Bandwidth Minimization Problem

This paper introduces weighted-BMP, a variant of the Bandwidth Minimization Problem (BMP), with a significant application in optimizing quantum emulation. Weighted-BMP optimizes particles ordering to reduce the emulation costs, by designing a particle interaction matrix where strong interactions are...

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Bibliographic Details
Published inarXiv.org
Main Authors M Yassine Naghmouchi, Vovrosh, Joseph, Wesley da Silva Coelho, Dauphin, Alexandre
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.04.2024
Subjects
Algorithms
Broken symmetry
Emulation
Integer programming
Linear programming
Lower bounds
Mixed integer
Numerical analysis
Optimization
Ordering tasks
Particle interactions
Physics - Quantum Physics
Solvers
Strong interactions (field theory)
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Summary:This paper introduces weighted-BMP, a variant of the Bandwidth Minimization Problem (BMP), with a significant application in optimizing quantum emulation. Weighted-BMP optimizes particles ordering to reduce the emulation costs, by designing a particle interaction matrix where strong interactions are placed as close as possible to the diagonal. We formulate the problem using a Mixed Integer Linear Program (MILP) and solve it to optimality with a state of the art solver. To strengthen our MILP model, we introduce symmetry-breaking inequalities and establish a lower bound. Through extensive numerical analysis, we examine the impacts of these enhancements on the solver's performance. The introduced reinforcements result in an average CPU time reduction of 25.61 percent. Additionally, we conduct quantum emulations of realistic instances. Our numerical tests show that the weighted-BMP approach outperforms the Reverse Cuthill-McKee (RCM) algorithm, an efficient heuristic used for site ordering tasks in quantum emulation, achieving an average memory storage reduction of 24.48 percent. From an application standpoint, this study is the first to apply an exact optimization method, weighted-BMP, that considers interactions for site ordering in quantum emulation pre-processing, and shows its crucial role in cost reduction. From an algorithmic perspective, it contributes by introducing important reinforcements and lays the groundwork for future research on further enhancements, particularly on strengthening the weak linear relaxation of the MILP.
ISSN:2331-8422
DOI:10.48550/arxiv.2404.15165