Measurement-Guided State Refinement for Shallow Feedback-Based Quantum Optimization Algorithm

TL;DR

This paper introduces a measurement-guided initialization method for shallow quantum optimization algorithms, enhancing their performance on NISQ devices by iteratively refining solutions without classical parameter tuning.

Contribution

It proposes a novel measurement-guided initialization strategy integrated into FALQON, enabling iterative improvement of solutions in shallow-depth quantum circuits.

Findings

Measurement-guided initialization improves solution quality.

The method enables iterative refinement without classical optimization.

Performance gains demonstrated on weighted MaxCut instances.

Abstract

Limited circuit depth remains a central constraint for quantum optimization in the noisy intermediate-scale quantum (NISQ) regime, where shallow unitary dynamics may fail to sufficiently concentrate probability on low-energy configurations. We introduce Measurement-Guided Initialization (MGI), an iterative strategy that uses measurement outcomes from previous executions to update the initialization of subsequent runs. The method extracts single-qubit marginal probabilities from dominant measurement outcomes and prepares a biased product-state initialization, allowing information obtained during optimization to be reused without introducing classical parameter optimization. We implement this approach in the context of the Feedback-Based Algorithm for Quantum Optimization (FALQON) and evaluate its performance on weighted MaxCut instances. Numerical results show that measurement-guided initialization improves the performance of shallow-depth circuits and enables iterative refinement toward high-quality solutions while preserving the non-variational structure of the algorithm. These results indicate that measurement statistics can be exploited to improve shallow quantum optimization protocols compatible with NISQ devices.