Pure MaxSAT and Its Applications to Combinatorial Optimization via Linear Local Search

Zhang, Xindi

doi:10.1007/978-3-030-58475-7_6

Cited by 3 publications

(1 citation statement)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These SAT instances are then solved by sequentially calling a SAT solver [1,5]. Numerous variants of SAT-based MaxSAT algorithms are presented in [7]. State-of-the-art algorithms that aim to solve either SAT or MaxSAT are tested on international competitions such as the SAT competition and the MaxSAT evaluation (MSE) [8].…”

Section: Introductionmentioning

confidence: 99%

Finding solutions to MaxSAT in a quantum computer

Clemente,

Venegas-Andraca

2024

Preprint

View full text Add to dashboard Cite

We introduce a quantum algorithm designed to encode a 3-MaxSAT instance f(z) comprising n Boolean variables and m clauses. In the initial stage, we construct an unitary operator F ∈ SU(2n) whose corresponding eigenvalues are phase-encoded to reflect the total count of non-satisfiable clauses observed when evaluating f(z) under a truth assignment (a potential solution) ϕj . Our second stage consists in combining F along Quantum Phase Estimation to map the induced phase shifts into measurable quantum states in only O(mlog(m)) time due to commuting properties of F. Our objective is to identify a state |ϕj⟩ with the smallest phase shift induced by F. Such eigenstate |ϕj⟩ directly corresponds to the truth assignment minimizing the count of non-satisfiable clauses, thereby constituting our solution for f(z). We demonstrate how we can use this encoding along with Amplitude Amplification to find such solutions to MaxSAT in O(mlog(m)1.414n) time. In perspective, this search algorithm may represent an exponential speedup over MaxSAT algorithms, whose complexity grows exponentially as a function of the number of clauses.

show abstract