Quantum annealing with anneal path control: application to 2-SAT problems with known energy landscapes

TL;DR

This paper investigates how anneal path control on the D-Wave 2000Q quantum annealer can significantly improve the success probability of solving 2-SAT problems by widening the spectral gap and optimizing annealing schemes.

Contribution

It introduces and analyzes the impact of anneal path control, a new feature, on quantum annealing performance for specific optimization problems with known energy landscapes.

Findings

Anneal path control can increase the spectral gap by one or two orders of magnitude.

Adjusting the anneal path improves the success probability of finding solutions.

Iterative methods based on spin properties enhance quantum annealing efficiency.

Abstract

We study the effect of the anneal path control per qubit, a new user control feature offered on the D-Wave 2000Q quantum annealer, on the performance of quantum annealing for solving optimization problems by numerically solving the time-dependent Schr\"odinger equation for the time-dependent Hamiltonian modeling the annealing problems. The anneal path control is thereby modeled as a modified linear annealing scheme, resulting in an advanced and retarded scheme. The considered optimization problems are 2-SAT problems with 12 Boolean variables, a known unique ground state and a highly degenerate first excited state. We show that adjustment of the anneal path control can result in a widening of the minimal spectral gap by one or two orders of magnitude and an enhancement of the success probability of finding the solution of the optimization problem. We scrutinize various iterative methods based on the spin floppiness, the average spin value, and on the average energy and describe their performance in boosting the quantum annealing process.