Rank-Dependent Error Bounds and Near-Optimality in Quantum Control via Hierarchical Tucker Surrogates

Abstract:We develop a certified finite-horizon quantum optimal-control framework based on fixed-rank Hierarchical Tucker (HT) surrogates. Under a uniform rank-dependent HT truncation-accuracy condition, we establish exponentially decaying trajectory, cost, and value-function errors and near-optimality of surrogate-generated controls. We further derive a logarithmic rank--performance relation, an a posteriori cost certificate from realized truncation perturbations, and guarantees for inexact surrogate optimization and control convergence under additional regularity conditions. Numerical experiments on controlled XXZ spin chains provide finite-sample evidence consistent with the truncation condition and illustrate the trade-off between HT rank, representation size, surrogate accuracy, and control performance.

Optimization and Control (math.OC); Quantum Physics (quant-ph)

arXiv:2609.14686 [math.OC]

(or arXiv:2609.14686v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2609.14686 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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