REDUCING DISCRETE OPTIMIZATION PROBLEMS TO THE QUBO FORM

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Abstract

Practical discrete optimization problems often contain multidimensional arrays of variables with linear constraints, which complicates their conversion to QUBO (quadratic unconstrained binary optimization) form. The article proposes a systematic approach to transforming such problems, which includes three key steps: the transition from a multidimensional representation of variables to a one-dimensional one using the Kronecker product of matrices, the reduction of mixed variables to binary ones, and the introduction of linear constraints into the objective function through quadratic penalties. Explicit computational formulas are obtained for each stage, simplifying their software implementation. The developed method is illustrated with examples from graph theory and combinatorial optimization, including classical formulations, confirming its universality. The results of the article allow standardizing the process of adapting problems for solving on quantum annealing algorithms (e.g., D-Wave) and classical QUBO solvers.

About the authors

A. M Semenov

Russian Quantum Center; "Cloud Quantum Technologies" LLC

Email: a.semenov@rqc.ru
Moscow; Moscow

S. R Usmanov

Russian Quantum Center; "Cloud Quantum Technologies" LLC

Email: s.usmanov@rqc.ru
Moscow; Moscow

A. K Fedorov

Russian Quantum Center; "Cloud Quantum Technologies" LLC

Email: akf@rqc.ru
Moscow; Moscow

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