SAT, Gadgets, Max2XOR, and Quantum Annealers
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.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2403.00182
 arXiv:
 arXiv:2403.00182
 Bibcode:
 2024arXiv240300182A
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity;
 Computer Science  Logic in Computer Science
 EPrint:
 arXiv admin note: text overlap with arXiv:2204.01774