QAOA-PCA: Enhancing Efficiency in the Quantum Approximate Optimization Algorithm via Principal Component Analysis

TL;DR

QAOA faces scalability challenges as the number of QAOA layers increases, since the parameter space grows with $2p$ and optimization becomes costly. The authors propose QAOA-PCA, a PCA-based reparameterization that learns principal components from optimized parameters on small graphs and uses them to represent larger-instance parameters with far fewer degrees of freedom. Across a large training set of graphs and a substantial evaluation set, QAOA-PCA significantly reduces the number of optimizer iterations while maintaining competitive performance, outperforming standard QAOA when parameter counts are matched. The work highlights a practical path to scaling QAOA on near-term devices by trading a small amount of optimality for substantial gains in optimization efficiency, and outlines concrete future directions for adaptive component counts and hardware experiments.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational algorithm for solving combinatorial optimization problems on near-term devices. However, as the number of layers in a QAOA circuit increases, which is correlated with the quality of the solution, the number of parameters to optimize grows linearly. This results in more iterations required by the classical optimizer, which results in an increasing computational burden as more circuit executions are needed. To mitigate this issue, we introduce QAOA-PCA, a novel reparameterization technique that employs Principal Component Analysis (PCA) to reduce the dimensionality of the QAOA parameter space. By extracting principal components from optimized parameters of smaller problem instances, QAOA-PCA facilitates efficient optimization with fewer parameters on larger instances. Our empirical evaluation on the prominent MaxCut problem demonstrates that QAOA-PCA consistently requires fewer iterations than standard QAOA, achieving substantial efficiency gains. While this comes at the cost of a slight reduction in approximation ratio compared to QAOA with the same number of layers, QAOA-PCA almost always outperforms standard QAOA when matched by parameter count. QAOA-PCA strikes a favorable balance between efficiency and performance, reducing optimization overhead without significantly compromising solution quality.

Figures (1)

• Figure 1: Distributions of the number of iterations (x-axis) and approximation ratios (y-axis) for QAOA-PCA (blue), standard QAOA with the same number of layers (orange), and standard QAOA with the same number of parameters (green).