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From Projected Subspaces to Full-Space Implementations: Representation-Equivalence Audits for Open-Shell ADAPT-VQE — arXiv:2609.36060

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.36060
License (as archived): CC0-1.0
Archived: 2026-10-07T19:26:18.985Z
SHA-256 of the archived text: 94469fd03da446bdcbcab8964a600a6302df05c3d301803a44a021762f4ed5ba
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How to cite

From Projected Subspaces to Full-Space Implementations: Representation-Equivalence Audits for Open-Shell ADAPT-VQE — arXiv:2609.36060 — arXiv (en), https://arxiv.org/abs/2609.36060 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7a2abc70ddca (Metraipolis archive dc_7a2abc70ddca, sha256 94469fd03da446bdcbcab8964a600a6302df05c3d301803a44a021762f4ed5ba)

BibTeX

@misc{dc7a2abc70ddca,
  title = {From Projected Subspaces to Full-Space Implementations: Representation-Equivalence Audits for Open-Shell ADAPT-VQE — arXiv:2609.36060},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.36060},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7a2abc70ddca; sha256 94469fd03da446bdcbcab8964a600a6302df05c3d301803a44a021762f4ed5ba},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.36060. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A variational state optimized in a symmetry-projected space need not be the state prepared by exponentiating the corresponding unprojected parent generators. For an orthogonal target-space projector $P$, $Q=I-P$, and an anti-Hermitian generator $A$, exact equivalence for all amplitudes requires target-space invariance, $QAP=0$. We formulate this condition as a representation-equivalence audit for open-shell ADAPT-VQE. For a canonical CAS(15e,9o) type-1 Cu(II) Hamiltonian, 274 of 323 bare Hartree--Fock-origin single, double, and triple excitations violate this condition. Projected-doublet ADAPT reaches 1.5719 m$E_h$ with 121 operators, whereas the same amplitudes in the corresponding full-space sequence give 464.730 m$E_h$ error, 0.07343 fidelity with the projected state, and 54.45\% quartet weight. Reoptimizing the same 121 parent generators in the same order under the hard constraint $p_D\ge0.999$ reduces the best converged error to 8.482 m$E_h$, showing that the catastrophic same-angle failure is primarily a representation/parameter-transfer failure but is not completely repaired by full-space reoptimization of the fixed sequence. An independent 12-qubit NO benchmark exhibits the same mechanism more mildly. A spin-preserving generalized full-space construction removes the representation ambiguity and reaches 1.493 and 1.181 m$E_h$ at 18 and 24 qubits. For the 18-qubit positive control, selectively refining only four Suzuki-2 factors and re-transpiling with a fixed compiler seed passes the predeclared circuit-equivalence gate at 19,660 controlled-X (CX) gates and depth 23,016. Circuit synthesis and final-energy measurement therefore constitute separate validation layers. The contribution is a validation framework, not a new spin-adapted ADAPT algorithm.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-30 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.36060 — 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 2026-10-07T18:55:50.509Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).