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A variational quantum eigensolver-based cutting plane framework for semidefinite programming problems — arXiv:2609.02139

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.02139
License (as archived): CC0-1.0
Archived: 2026-10-17T05:25:54.562Z
SHA-256 of the archived text: ac071484a99e73554dec5573bb02366343696df95f291b377dca82e1b6c62bfe
Stable URL of this page: https://metraipolis.com/documento/dc_dbec16cb044e

How to cite

A variational quantum eigensolver-based cutting plane framework for semidefinite programming problems — arXiv:2609.02139 — arXiv (en), https://arxiv.org/abs/2609.02139 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dbec16cb044e (Metraipolis archive dc_dbec16cb044e, sha256 ac071484a99e73554dec5573bb02366343696df95f291b377dca82e1b6c62bfe)

BibTeX

@misc{dcdbec16cb044e,
  title = {A variational quantum eigensolver-based cutting plane framework for semidefinite programming problems — arXiv:2609.02139},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.02139},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dbec16cb044e; sha256 ac071484a99e73554dec5573bb02366343696df95f291b377dca82e1b6c62bfe},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.02139. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Semidefinite programming plays a key role in optimization, with broad impact across control theory, machine learning, and combinatorial optimization. Although semidefinite programs are polynomially solvable, several commonly used algorithms rest on a linear-algebraic step whose running time grows cubically with the matrix dimension and which requires the matrix itself to be held in memory, at quadratic cost. In this study, we propose replacing it with a variational quantum eigensolver, whose qubit requirement is logarithmic in the matrix dimension, and present the first end-to-end implementation of such an approach within a cutting-plane framework, together with an operator-derived ansatz whose entanglement structure is read directly from the Pauli support of the candidate matrix. Evaluated on the control family of SDPLIB against an identical scheme driven by an exact eigendecomposition, the variational oracle produces valid cuts throughout, closing 32 to 82% of the initial optimality gap against a near-constant 75 to 82% for the exact oracle. Implementing and measuring the method end to end surfaces several effects not visible from theoretical analyses alone: where memory is actually consumed, how the padding required to fit a matrix onto a quantum register can mislead the variational optimizer, and why the candidate matrices prove dense in the Pauli basis, reducing the operator-derived ansatz to full entanglement. We report these findings and discuss their implications for near-term hybrid quantum-classical approaches.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-03 in math.OC).
Categorie arXiv: Quantum Physics (quant-ph) ; Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2609.02139 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T04:44:15.069Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-03?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).