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PreprintCC BY 4.0arXiv

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

  • Nahid Binandeh Dehaghani
  • Rafal Wisniewski
  • Julian Berberich
  • A. Pedro Aguiar
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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.

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Cite

BibTeXRIS
BibTeX
@misc{dehaghani2026rankdependent,
  title = {{Rank-Dependent Error Bounds and Near-Optimality in Quantum Control via Hierarchical Tucker Surrogates}},
  author = {Nahid Binandeh Dehaghani and Rafal Wisniewski and Julian Berberich and A. Pedro Aguiar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14686},
  eprint = {2609.14686},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14686},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Rank-Dependent Error Bounds and Near-Optimality in Quantum Control via Hierarchical Tucker Surrogates
AU  - Nahid Binandeh Dehaghani
AU  - Rafal Wisniewski
AU  - Julian Berberich
AU  - A. Pedro Aguiar
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14686
UR  - https://arxiv.org/abs/2609.14686
AB  - 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.
ER  -