Pauli Correlation Encoding for Budget-Constrained Optimization

TL;DR

This paper extends Pauli Correlation Encoding (PCE) for constrained quantum optimization, introduces an iterative strategy to improve constraint satisfaction, and demonstrates its effectiveness across various problem sizes in the NISQ era.

Contribution

It adapts PCE to constrained problems and proposes an iterative approach that enhances constraint enforcement and solution quality.

Findings

Iterative-$mbda$ PCE improves constraint satisfaction.

The iterative method yields better cut sizes.

Standard PCE struggles with constraint enforcement.

Abstract

Quantum optimization has gained increasing attention as advances in quantum hardware enable the exploration of problem instances approaching real-world scale. Among existing approaches, variational quantum algorithms and quantum annealing dominate current research; however, both typically rely on one-hot encodings that severely limit scalability. Pauli Correlation Encoding (PCE) was recently introduced as an alternative paradigm that reduces qubit requirements by embedding problem variables into Pauli correlations. Despite its promise, PCE has not yet been studied in the context of constrained optimization. In this work, we extend the PCE framework to constrained combinatorial optimization problems and evaluate its performance across multiple problem sizes. Our results show that the standard PCE formulation struggles to reliably enforce constraints, which motivates the introduction of the Iterative-$\alpha$ PCE. This iterative strategy significantly improves solution quality, achieving consistent constraint satisfaction while yielding better cut sizes across a wide range of instances. These findings highlight both the limitations of current PCE formulations for constrained problems and the effectiveness of iterative strategies for advancing quantum optimization in the NISQ era.