Compressed Quadratization of Higher Order Binary Optimization Problems
Abstract
Recent hardware advances in quantum and quantuminspired annealers promise substantial speedup for solving NPhard combinatorial optimization problems compared to generalpurpose computers. These specialpurpose hardware are built for solving hard instances of Quadratic Unconstrained Binary Optimization (QUBO) problems. In terms of number of variables and precision of these hardware are usually resourceconstrained and they work either in Ising space {1,1} or in Boolean space {0,1}. Many naturally occurring problem instances are higherorder in nature. The known method to reduce the degree of a higherorder optimization problem uses Rosenberg's polynomial. The method works in Boolean space by reducing the degree of one term by introducing one extra variable. In this work, we prove that in Ising space the degree reduction of one term requires the introduction of two variables. Our proposed method of degree reduction works directly in Ising space, as opposed to converting an Ising polynomial to Boolean space and applying previously known Rosenberg's polynomial. For sparse higherorder Ising problems, this results in a more compact representation of the resultant QUBO problem, which is crucial for utilizing resourceconstrained QUBO solvers.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 DOI:
 10.48550/arXiv.2001.00658
 arXiv:
 arXiv:2001.00658
 Bibcode:
 2020arXiv200100658M
 Keywords:

 Quantum Physics;
 Computer Science  Discrete Mathematics