# Assessing Solution Quality of 3SAT on a Quantum Annealing Platform

## TL;DR

This paper investigates how the difficulty of 3SAT instances affects the solution quality of quantum annealers, revealing that classical phase transition phenomena influence quantum performance.

## Contribution

It is the first to analyze the impact of 3SAT problem complexity on quantum annealing solution quality, highlighting the persistence of phase transition effects.

## Key findings

- Quantum annealers' solution quality varies with problem difficulty.
- The classical phase transition in 3SAT influences quantum annealing performance.
- Solution accuracy decreases near the phase transition region.

## Abstract

When solving propositional logic satisfiability (specifically 3SAT) using quantum annealing, we analyze the effect the difficulty of different instances of the problem has on the quality of the answer returned by the quantum annealer. A high-quality response from the annealer in this case is defined by a high percentage of correct solutions among the returned answers. We show that the phase transition regarding the computational complexity of the problem, which is well-known to occur for 3SAT on classical machines (where it causes a detrimental increase in runtime), persists in some form (but possibly to a lesser extent) for quantum annealing.