Comparison of QAOA with Quantum and Simulated Annealing

TL;DR

This paper compares QAOA, Quantum Annealing, and Simulated Annealing on a class of problems, highlighting fundamental differences and identifying instances where QA and SA perform poorly compared to QAOA.

Contribution

It introduces a class of problems solvable by QAOA and demonstrates cases where QA and SA have exponentially small success probabilities, establishing a clear distinction among these methods.

Findings

QAOA outperforms QA and SA on certain spectral problem instances.

QA and SA have exponentially small success probabilities on specific problem classes.

The study delineates fundamental differences between interference-based and fluctuation-based heuristics.

Abstract

We present a comparison between the Quantum Approximate Optimization Algorithm (QAOA) and two widely studied competing methods, Quantum Annealing (QA) and Simulated Annealing (SA). To achieve this, we define a class of optimization problems with respect to their spectral properties which are exactly solvable with QAOA. In this class, we identify instances for which QA and SA have an exponentially small probability to find the solution. Consequently, our results define a first demarcation line between QAOA, Simulated Annealing and Quantum Annealing, and highlight the fundamental differences between an interference-based search heuristic such as QAOA and heuristics that are based on thermal and quantum fluctuations like SA and QA respectively.