The Quantum Alternating Operator Ansatz for Satisfiability Problems

TL;DR

This study compares various Quantum Alternating Operator Ansatz implementations for combinatorial optimization, revealing that traditional mixers perform best at larger sizes, while more complex mixers do not necessarily improve performance.

Contribution

It provides the first large-scale numerical comparison of over 100 QAOA implementations across different problem sizes and mixer types, correcting previous assumptions about mixer superiority.

Findings

Traditional transverse-field mixer performs best for 8-14 variables.

Grover mixer with thresholding excels at size 6.

More complex mixers may not enhance QAOA performance.

Abstract

We comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial optimization problems. Our survey includes over 100 different mixing unitaries, and we combine each mixer with both the standard phase separator unitary representing the objective function and a thresholded version. Our numerical tests for randomly chosen instances of the unconstrained optimization problems Max 2-SAT and Max 3-SAT reveal that the traditional transverse-field mixer with the standard phase separator performs best for problem sizes of 8 through 14 variables, while the recently introduced Grover mixer with thresholding wins at problems of size 6. This result (i) corrects earlier work suggesting that the Grover mixer is a superior mixer based only on results from problems of size 6, thus illustrating the need to push numerical simulation to larger problem sizes to more accurately predict performance; and (ii) it suggests that more complicated mixers and phase separators may not improve QAOA performance.