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Frontiers in Computer Science
Article . 2023 . Peer-reviewed
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Frontiers in Computer Science
Article . 2023
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Article . 2023
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Posiform planting: generating QUBO instances for benchmarking

Authors: Georg Hahn; Elijah Pelofske; Hristo N. Djidjev; Hristo N. Djidjev;

Posiform planting: generating QUBO instances for benchmarking

Abstract

We are interested in benchmarking both quantum annealing and classical algorithms for minimizing quadratic unconstrained binary optimization (QUBO) problems. Such problems are NP-hard in general, implying that the exact minima of randomly generated instances are hard to find and thus typically unknown. While brute forcing smaller instances is possible, such instances are typically not interesting due to being too easy for both quantum and classical algorithms. In this contribution, we propose a novel method, called posiform planting, for generating random QUBO instances of arbitrary size with known optimal solutions, and use those instances to benchmark the sampling quality of four D-Wave quantum annealers utilizing different interconnection structures (Chimera, Pegasus, and Zephyr hardware graphs) and the simulated annealing algorithm. Posiform planting differs from many existing methods in two key ways. It ensures the uniqueness of the planted optimal solution, thus avoiding groundstate degeneracy, and it enables the generation of QUBOs that are tailored to a given hardware connectivity structure, provided that the connectivity is not too sparse. Posiform planted QUBOs are a type of 2-SAT boolean satisfiability combinatorial optimization problems. Our experiments demonstrate the capability of the D-Wave quantum annealers to sample the optimal planted solution of combinatorial optimization problems with up to 5, 627 qubits.

Keywords

MAX-2-SAT, FOS: Computer and information sciences, time-to-solution, Quantum Physics, quantum annealing (QA), Statistical Mechanics (cond-mat.stat-mech), Computer Science - Emerging Technologies, FOS: Physical sciences, QA75.5-76.95, planted solution, QUBO problem, Emerging Technologies (cs.ET), combinatorial optimization problem, Electronic computers. Computer science, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Quantum Physics (quant-ph), Condensed Matter - Statistical Mechanics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green
gold