Computational Complexity of Quadratic Unconstrained Binary Optimization
Abstract
In this paper, we study the computational complexity of the quadratic unconstrained binary optimization (QUBO) problem under the functional problem FP^NP categorization. We focus on three subclasses: (1) When all coefficients are integers QUBO is FP^NPcomplete. When every coefficient is an integer lower bounded by a constant k, QUBO is FP^NP[log]complete. (3) When coefficients can only be in the set {1, 0, 1}, QUBO is again FP^NP[log]complete. With recent results in quantum annealing able to solve QUBO problems efficiently, our results provide a clear connection between quantum annealing algorithms and the FP^NP complexity class categorization. We also study the computational complexity of the decision version of the QUBO problem with integer coefficients. We prove that this problem is DPcomplete.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.10048
 Bibcode:
 2021arXiv210910048Y
 Keywords:

 Computer Science  Computational Complexity;
 Mathematics  Optimization and Control