A Parallel and Distributed Quantum SAT Solver Based on Entanglement and Quantum Teleportation

TL;DR

This paper introduces a novel parallel and distributed quantum SAT solver that significantly reduces per-iteration complexity using entanglement and quantum teleportation, enhancing scalability for large problems.

Contribution

It presents a new quantum SAT solving approach that leverages entanglement and teleportation to achieve constant-time clause evaluation and distributed computation across multiple quantum nodes.

Findings

Reduced time complexity from O(m) to O(1) per iteration.

Distributed quantum SAT solving across multiple nodes.

Validated correctness through simulations.

Abstract

Boolean satisfiability (SAT) solving is a fundamental problem in computer science. Finding efficient algorithms for SAT solving has broad implications in many areas of computer science and beyond. Quantum SAT solvers have been proposed in the literature based on Grover's algorithm. Although existing quantum SAT solvers can consider all possible inputs at once, they evaluate each clause in the formula one by one sequentially, making the time complexity O(m) -- linear to the number of clauses m -- per Grover iteration. In this work, we develop a parallel quantum SAT solver, which reduces the time complexity in each iteration from linear time O(m) to constant time O(1) by utilising extra entangled qubits. To further improve the scalability of our solution in case of extremely large problems, we develop a distributed version of the proposed parallel SAT solver based on quantum teleportation such that the total qubits required are shared and distributed among a set of quantum computers (nodes), and the quantum SAT solving is accomplished collaboratively by all the nodes. We have proved the correctness of our approaches and demonstrated them in simulations.