Solving Random Satisfiability Problems with Quantum Computers

TL;DR

This paper analyzes and improves a quantum algorithm for solving random satisfiability problems, demonstrating its superior performance over classical heuristics and unstructured quantum algorithms, especially near phase transitions.

Contribution

It provides an asymptotic analysis of the quantum algorithm's performance, incorporating amplitude variations, and shows how modifications based on this analysis enhance effectiveness.

Findings

Quantum algorithms outperform classical heuristics like GSAT.

Modified quantum algorithm shows improved success rates.

Performance remains good near phase transition points.

Abstract

Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average and variation of amplitudes among search states with the same costs. The analysis predicts good performance, on average, for a variety of problems including those near a phase transition associated with a high concentration of hard cases. Based on empirical evaluation for small problems, modifying the algorithm in light of this analysis improves its performance. The algorithm improves on both GSAT, a commonly used conventional heuristic, and quantum algorithms ignoring problem structure.