Posiform planting: generating QUBO instances for benchmarking

Hahn, Georg; Pelofske, Elijah; Djidjev, Hristo N.

doi:10.3389/fcomp.2023.1275948

Title: Posiform planting: generating QUBO instances for benchmarking

Journal Article · Tue Nov 21 00:00:00 EST 2023 · Frontiers in Computer Science

DOI:https://doi.org/10.3389/fcomp.2023.1275948· OSTI ID:2217616

Hahn, Georg; Pelofske, Elijah; Djidjev, Hristo N.

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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2217616

Alternate ID(s):: OSTI ID: 2305318

Report Number(s):: LA-UR-23-27170; 1275948

Journal Information:: Frontiers in Computer Science, Journal Name: Frontiers in Computer Science Vol. 5; ISSN 2624-9898

Publisher:: Frontiers Media SACopyright Statement

Country of Publication:: Switzerland

Language:: English

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Title: Posiform planting: generating QUBO instances for benchmarking

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