Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Zhang, Zewen; Paredes, Roger; Sundar, Bhuvanesh; Quiroga, David; Kyrillidis, Anastasios; Duenas-Osorio, Leonardo; Pagano, Guido; Hazzard, Kaden R. A.

doi:10.1088/2058-9565/ad895c

Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Journal Article · Mon Nov 04 00:00:00 EST 2024 · Quantum Science and Technology

DOI:https://doi.org/10.1088/2058-9565/ad895c· OSTI ID:2475890

; Paredes, Roger; ; Quiroga, David; Kyrillidis, Anastasios; Duenas-Osorio, Leonardo; ;

Abstract

The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0023806; SC0024301

OSTI ID:: 2475890

Alternate ID(s):: OSTI ID: 2472975

Journal Information:: Quantum Science and Technology, Journal Name: Quantum Science and Technology Journal Issue: 1 Vol. 10; ISSN 2058-9565

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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