Optimal sufficient requirements on the embedded Ising problem in polynomial time
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Published:2023-08-08
Issue:8
Volume:22
Page:
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ISSN:1573-1332
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Container-title:Quantum Information Processing
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language:en
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Short-container-title:Quantum Inf Process
Author:
Lobe ElisabethORCID, Kaibel Volker
Abstract
AbstractOne of the central applications for quantum annealers is to find the solutions of Ising problems. Suitable Ising problems, however, need to be formulated such that they, on the one hand, respect the specific restrictions of the hardware and, on the other hand, represent the original problems which shall actually be solved. We evaluate sufficient requirements on such an embedded Ising problem analytically and transform them into a linear optimization problem. With an objective function aiming to minimize the maximal absolute problem parameter, the precision issues of the annealers are addressed. Due to the redundancy of several constraints, we can show that the formally exponentially large optimization problem can be reduced and finally solved in polynomial time for the standard embedding setting where the embedded vertices induce trees. This allows to formulate provably equivalent embedded Ising problems in a practical setup.
Funder
Bundesministerium für Wirtschaft und Klimaschutz (BMWK) DLR Quantum Computing Initiative
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Modeling and Simulation,Signal Processing,Theoretical Computer Science,Statistical and Nonlinear Physics,Electronic, Optical and Magnetic Materials
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