Max-flow min-cut theorem in quantum computing

Nongmeikapam Brajabidhu Singh, Arnab Roy and Anish Kumar Saha

Physica A: Statistical Mechanics and its Applications, 2024, vol. 649, issue C

Abstract: The max-flow min-cut theorem in graph theory states that the maximum flow of a network is equal to the minimum cut of edges of the flow network. Max-flow and min-cut are related as two primal–dual linear programs. The theorem is applicable in applications like network connectivity, graph matching problems, transportation and logistics, and scheduling problems. The aim of the paper is to model the classical max-flow and min-cut theorem in quantum computing. Two well-known methods for quantum optimization are quantum annealing and quantum approximate optimization algorithm. The max-flow min-cut is converted to its equivalent model of the above two methods for execution in polynomial time. This paper shows detailed classical to quantum conversion, analysis, implementation, and result of the theorem.

Keywords: Max-flow min-cut theorem; Quadratic unconstrained binary optimization; Ising model; Quantum annealing; Quantum approximate optimization algorithm (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:649:y:2024:i:c:s0378437124004990

DOI: 10.1016/j.physa.2024.129990

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