HyQSAT: A Hybrid Approach for 3-SAT Problems by Integrating Quantum Annealer with CDCL

Propositional satisfiability problem (SAT) is represented in a conjunctive normal form with multiple clauses, which is an important non-deterministic polynomial-time (NP) complete problem that plays a major role in various applications including artificial intelligence, graph colouring, and circuit analysis. Quantum annealing (QA) is a promising methodology for solving complex SAT problems by exploiting the parallelism of quantum entanglement, where the SAT variables are embedded to the qubits. However, the long embedding time fundamentally limits existing QA-based methods, leading to inefficient hardware implementation and poor scalability.

In this paper, we propose HyQSAT, a hybrid approach that integrates QA with the classical Conflict-Driven Clause Learning (CDCL) algorithm to enable end-to-end acceleration for solving SAT problems. Instead of embedding all clauses to QA hardware, we quantitatively estimate the conflict frequency of clauses and apply breadth-first traversal to choose their embedding order. We also consider the hardware topology to maximize the utilization of physical qubits in embedding to QA hardware. Besides, we adjust the embedding coefficients to improve the computation accuracy under qubit noise. Finally, we present how to interpret the satisfaction probability based on QA energy distribution and use this information to guide the CDCL search. Our experiments demonstrate that HyQSAT can effectively support larger-scale SAT problems that are beyond the capability of existing QA approaches, achieve up to 12.62X end-to-end speedup using D-Wave 2000Q compared to the classic CDCL algorithm on Intel E5 CPU, and considerably reduce the QA embedding time from 17.2s to 15.7µs compared to the D-Wave Minorminer algorithm [11].