Measurement-driven quantum computing: Performance of a 3-SAT solver

TL;DR

This paper explores a quantum algorithm for solving 3-SAT problems, demonstrating that it can outperform classical solvers in small systems by using measurement-driven evolution and parameter control.

Contribution

It introduces a measurement-driven quantum approach with parameter evolution that competes with classical 3-SAT solvers in small system simulations.

Findings

Quantum algorithm achieves competitive performance on small 3-SAT instances.

Parameter control influences success probability and runtime.

Quantum approach outperforms brute-force Grover's search in tested cases.

Abstract

We investigate the performance of a quantum algorithm for solving classical 3-SAT problems. A cycle of post-selected measurements drives the computer's register monotonically toward a steady state which is correlated to the classical solution(s). An internal parameter $\theta$ determines both the degree of correlation and the success probability, thus controlling the algorithm's runtime. Optionally this parameter can be gradually evolved during the algorithm's execution to create a Zeno-like effect; this can be viewed as an adiabatic evolution of a Hamiltonian which remains frustration-free at all points, and we lower-bound the corresponding gap. In exact numerical simulations of small systems up to 34 qubits our approach competes favourably with a high-performing classical 3-SAT solver, which itself outperforms a brute-force application of Grover's search.