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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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
23.04.2024
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Subjects | |
Online Access | Get full text |
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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. |
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DOI: | 10.48550/arxiv.2404.15165 |