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Physical Review A

Space-efficient quantum solvers for Boolean satisfiability problems via structural reduction

Quanfeng Lu, Shijie Wei, Jinfeng Zeng, Wentao Yang, Muxi Zheng, 常培杰, Dong Ruan, Zeguo Wang, Guilu Long

Published Oct 15, 2026• 1 citation
Publisher
DOI
10.1103/r3c5-4ldp

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Achieving quantum advantage remains a milestone in the noisy intermediate-scale quantum era. Without complexity proofs, scaling advantage—where quantum resource requirements grow more slowly than their classical counterparts—is the primary indicator. However, direct applications of quantum optimization algorithms to classically intractable problems have yet to demonstrate this advantage. Here we develop enhanced quantum solvers for the NP-complete one-in-three Boolean satisfiability problem. We propose a restricting space reduction algorithm that achieves optimal search-space dimensionality under mod-2 arithmetic, thereby reducing qubit requirements and time complexity. Numerical studies on instances with up to 70 variables demonstrate that our enhanced quantum approximate optimization algorithm- and quantum adiabatic algorithm-based solvers outperform state-of-the-art classical solvers; the quantum adiabatic algorithm-based solver serves as a lower-bound reference while retaining scaling advantage. Furthermore, experiments on a 13-qubit superconducting processor confirm the predicted improvements. Collectively, our results provide empirical evidence of quantum speedup for an NP-complete problem. This study develops enhanced quantum solvers for an NP-complete Boolean satisfiability problem and reports empirical scaling advantages over leading classical solvers in large-scale simulations, with supporting validation on a superconducting quantum processor.
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