Benchmark of Pauli Correlation Encoding for different optimisation problems

Abstract

The continuous progress of quantum technologies has spurred the exploration of their potential applications across diverse fields, particularly in combinatorial optimisation. In this work, we study a quantum-classical optimisation framework based on Pauli Correlation Encoding, an encoding scheme that can represent m binary variables using a polynomial number of qubits. To evaluate the performance of the method, we use three classical optimisation problems against the instances of the QOPTLib benchmark. The study includes an analysis of the impact of the compression order of the encoding scheme, the problem structure, and hyperparameter selection on solution quality, as well as the role of post-processing in improving performance. Additionally, we study the effect of shot-based execution and hardware noise, showing how these factors influence both the accuracy of expected value estimation and the overall dynamics of the optimisation process. The results indicate that the proposed PCE-based framework achieves competitive performance against the benchmark and, in several cases, obtains equivalent or even superior solutions, highlighting its potential as an efficient encoding strategy for quantum optimisation in the NISQ and near fault-tolerant era.