A parallel and distributed fixed-point quantum search algorithm for solving SAT problems

TL;DR

This paper introduces a parallel fixed-point quantum search algorithm for SAT problems that reduces circuit depth and is suitable for NISQ-era quantum computers by exploiting entanglement and distributed processing.

Contribution

It presents a novel parallel fixed-point quantum search method that processes SAT clauses independently and can be implemented in a distributed manner, addressing limitations of Grover's algorithm.

Findings

Reduces circuit depth by exploiting entanglement.

Enables distributed implementation of the quantum search.

Suitable for noisy intermediate-scale quantum (NISQ) devices.

Abstract

Boolean satisfiability (SAT) problem is of fundamental importance in computer science and many application domains. For Grover's algorithm, solving the SAT problem requires $\mathcal{O}(\sqrt{2^n})$ queries--where n denotes the number of logic variables in the problem. However, Grover's algorithm suffers from the Souffle problem: specifically, when the number of solutions is unknown, terminating the algorithm too early or too late leads to a significant reduction in the probability of obtaining a solution. In this paper, we propose a parallel fixed-point (PFP) search algorithm to solve the SAT problem. By exploiting entanglement, each clause in the conjunctive normal form (CNF) formula can be processed independently, leading to a significant reduction in circuit depth. We also discuss how to perform the algorithm in distributed manner. These make the PFPS algorithm particularly suitable for the noisy intermediate-scale quantum (NISQ) era.