Sampling diverse near-optimal solutions via algorithmic quantum annealing

TL;DR

This paper introduces a new diversity measure and benchmarking metrics for quantum annealing solvers, demonstrating that inhomogeneous schedules and non-equilibrium quantum fluctuations can significantly improve the sampling of diverse near-optimal solutions in complex optimization problems.

Contribution

It proposes a novel diversity metric and time-to-diversity measure, and shows how advanced quantum annealing strategies enhance solution diversity and reduce problem hardness.

Findings

Inhomogeneous quantum annealing schedules outperform standard schedules in solution diversity.

Non-equilibrium quantum fluctuations reduce the fraction of hard instances by over 25%.

Solution diversity can be increased by up to 40% using quantum phase transitions.

Abstract

Sampling a diverse set of high-quality solutions for hard optimization problems is of great practical relevance in many scientific disciplines and applications, such as artificial intelligence and operations research. One of the main open problems is the lack of ergodicity, or mode collapse, for typical stochastic solvers based on Monte Carlo techniques leading to poor generalization or lack of robustness to uncertainties. Currently, there is no universal metric to quantify such performance deficiencies across various solvers. Here, we introduce a new diversity measure for quantifying the number of independent approximate solutions for NP-hard optimization problems. Among others, it allows benchmarking solver performance by a required time-to-diversity (TTD), a generalization of often used time-to-solution (TTS). We illustrate this metric by comparing the sampling power of various quantum annealing strategies. In particular, we show that the inhomogeneous quantum annealing schedules can redistribute and suppress the emergence of topological defects by controlling space-time separated critical fronts, leading to an advantage over standard quantum annealing schedules with respect to both TTS and TTD for finding rare solutions. Using path-integral Monte Carlo simulations for up to 1600 qubits, we demonstrate that nonequilibrium driving of quantum fluctuations, guided by efficient approximate tensor network contractions, can significantly reduce the fraction of hard instances for random frustrated 2D spin-glasses with local fields. Specifically, we observe that by creating a class of algorithmic quantum phase transitions, the diversity of solutions can be enhanced by up to 40% with the fraction of hard-to-sample instances reducing by more than 25%.