SAT, Gadgets, Max2XOR, and Quantum Annealers

TL;DR

This paper explores how quantum annealers can be used to solve SAT problems by reducing them to Max2XOR problems through the construction of gadgets, enabling translation into quantum annealer configurations.

Contribution

It introduces gadgets for reducing SAT to Max2XOR, facilitating the use of quantum annealers for SAT solving.

Findings

Gadgets effectively reduce SAT to Max2XOR.

Method enables translation of SAT instances to quantum annealer configurations.

Supports potential quantum advantage in solving SAT problems.

Abstract

Quantum Annealers are basically quantum computers that with high probability can optimize certain quadratic functions on Boolean variables in constant time. These functions are basically the Hamiltonian of Ising models that reach the ground energy state, with a high probability, after an annealing process. They have been proposed as a way to solve SAT. These Hamiltonians can be seen as Max2XOR problems, i.e. as the problem of finding an assignment that maximizes the number of XOR clauses of at most 2 variables that are satisfied. In this paper, we present several gadgets to reduce SAT to Max2XOR. We show how they can be used to translate SAT instances to initial configurations of a quantum annealer.