Compressed Quadratization of Higher Order Binary Optimization Problems
| Autor: | Arnab Roy, Hayato Ushijima-Mwesigwa, Avradip Mandal, Sarvagya Upadhyay |
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| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Quantum Physics Polynomial 021103 operations research Speedup Optimization problem Discrete Mathematics (cs.DM) Degree (graph theory) Computer science Quantum annealing 0211 other engineering and technologies FOS: Physical sciences 02 engineering and technology 01 natural sciences Algebra Reduction (complexity) 0103 physical sciences Quadratic unconstrained binary optimization Ising model Quantum Physics (quant-ph) 010306 general physics Representation (mathematics) Algorithm Computer Science - Discrete Mathematics Variable (mathematics) |
| Zdroj: | DCC CF |
| DOI: | 10.1109/dcc47342.2020.00090 |
| Popis: | Recent hardware advances in quantum and quantum-inspired annealers promise substantial speedup for solving NP-hard combinatorial optimization problems compared to general-purpose computers. These special-purpose 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 resource-constrained and they work either in Ising space {-1, 1} or in Boolean space {0, 1}. Many naturally occurring problem instances are higher-order in nature. The known method to reduce the degree of a higher-order 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 higher-order Ising problems, this results in a more compact representation of the resultant QUBO problem, which is crucial for utilizing resource-constrained QUBO solvers. |
| Databáze: | OpenAIRE |
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