Local Search Methods for Quantum Computers

TL;DR

This paper explores how quantum computers can implement local search algorithms for NP-hard problems, demonstrating their effectiveness on SAT instances, especially highly constrained ones, through empirical evaluation.

Contribution

It introduces a local quantum search method that leverages neighborhood relations, providing empirical evidence of its performance on SAT problems.

Findings

Effective for highly constrained SAT instances

Less effective than incremental quantum methods for intermediate constraints

Uses smaller search space compared to other quantum methods

Abstract

Local search algorithms use the neighborhood relations among search states and often perform well for a variety of NP-hard combinatorial search problems. This paper shows how quantum computers can also use these neighborhood relations. An example of such a local quantum search is evaluated empirically for the satisfiability (SAT) problem and shown to be particularly effective for highly constrained instances. For problems with an intermediate number of constraints, it is somewhat less effective at exploiting problem structure than incremental quantum methods, in spite of the much smaller search space used by the local method.