Uncertain fate of fair sampling in quantum annealing

TL;DR

This paper investigates the fairness of sampling in quantum annealing, revealing that complex driver Hamiltonians do not necessarily improve sampling bias, and quantum annealers may not be ideal for sampling tasks.

Contribution

The study provides a detailed analysis of (un)fair sampling mechanisms in quantum annealing, showing limitations of advanced driver Hamiltonians and evaluating their effectiveness through simulations.

Findings

Higher-order driver terms do not always improve sampling fairness.

Quantum Monte Carlo simulations show comparable performance between quadratic and transverse-field drivers.

Quantum annealers may require post-processing for effective sampling applications.

Abstract

Recently, it was demonstrated both theoretically and experimentally on the D-Wave quantum annealer that transverse-field quantum annealing does not find all ground states with equal probability. In particular, it was proposed that more complex driver Hamiltonians beyond transverse fields might mitigate this shortcoming. Here, we investigate the mechanisms of (un)fair sampling in quantum annealing. While higher-order terms can improve the sampling for selected small problems, we present multiple counterexamples where driver Hamiltonians that go beyond transverse fields do not remove the sampling bias. Using perturbation theory we explain why this is the case. In addition, we present large-scale quantum Monte Carlo simulations for spin glasses with known degeneracy in two space dimensions and demonstrate that the fair-sampling performance of quadratic driver terms is comparable to standard transverse-field drivers. Our results suggest that quantum annealing machines are not well suited for sampling applications, unless post-processing techniques to improve the sampling are applied.