Hamiltonian-Guided Leverage Embedding: Robust Subspace Compression for Efficient QAOA Parameter Estimation

Abstract:The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical framework for combinatorial optimization on near-term quantum devices. A central bottleneck is the classical estimation of its variational parameters {\gamma} and {\beta}, which must be optimized over a high-dimensional, non-convex landscape corrupted by sampling noise. We observe that the classical feature matrices constructed from QAOA measurement samples exhibit pronounced low-rank structure, and exploit this property for noise-robust, reduced-dimension parameter search. We present the Hamiltonian-Guided Leverage Embedding (HGLE) algorithm - a hybrid pipeline that encodes low-energy quantum samples into a weighted Ising feature matrix and compresses it via leverage-score row sampling, provably preserving the dominant rank-rsubspace geometry. The compressed representation drives a classical trust-region loop for ({\gamma}, {\beta}) estimation at a fraction of the original cost. We provide formal guarantees for rank preservation and energy approximation error, and demonstrate robustness across problem types (Max-Cut, Maximum Independent Set) and graph topologies of varying density.

arXiv:2606.07814 [quant-ph]

(or arXiv:2606.07814v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.07814 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.