Quantum-Assisted Greedy Algorithms

TL;DR

This paper introduces a quantum-assisted greedy algorithm that leverages quantum annealers to improve candidate selection in greedy algorithms, demonstrating superior solutions on a D-Wave quantum processor.

Contribution

The paper presents a novel quantum-assisted greedy algorithm (QAGA) that integrates quantum annealing into classical greedy methods for combinatorial optimization.

Findings

QAGA outperforms traditional heuristics in solution quality

Quantum annealers effectively estimate variable probability distributions

Empirical results show improved solutions on D-Wave hardware

Abstract

We show how to leverage quantum annealers (QAs) to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at each stage, we use QAs that sample from the ground state of problem-dependent Hamiltonians at cryogenic temperatures and use retrieved samples to estimate the probability distribution of problem variables. More specifically, we look at each spin of the Ising model as a random variable and contract all problem variables whose corresponding uncertainties are negligible. Our empirical results on a D-Wave 2000Q quantum processor demonstrate that the proposed quantum-assisted greedy algorithm (QAGA) scheme can find notably better solutions compared to the state-of-the-art techniques in the realm of quantum annealing