MAX 2-SAT with up to 108 qubits

TL;DR

This study evaluates the performance of a 108-qubit quantum annealer on MAX 2-SAT problems, revealing its sensitivity to problem parameters and comparing it with classical algorithms.

Contribution

First experimental analysis of a large-scale quantum annealer on MAX 2-SAT, highlighting its performance scaling and problem hardness correlation.

Findings

DW1 performance scales favorably with problem size

DW1 is sensitive to the critical clause density

Performance correlation with classical solver is negligible

Abstract

We experimentally study the performance of a programmable quantum annealing processor, the D-Wave One (DW1) with up to 108 qubits, on maximum satisfiability problem with 2 variables per clause (MAX 2-SAT) problems. We consider ensembles of random problems characterized by a fixed clause density, an order parameter which we tune through its critical value in our experiments. We demonstrate that the DW1 is sensitive to the critical value of the clause density. The DW1 results are verified and compared with akmaxsat, an exact, state-of-the-art algorithm. We study the relative performance of the two solvers and how they correlate in terms of problem hardness. We find that the DW1 performance scales more favorably with problem size and that problem hardness correlation is essentially non-existent. We discuss the relevance and limitations of such a comparison.