PreprintarXiv licencearXiv
Universal holonomic control of algebras of observables
Abstract
We extend geometric parallel transport from states and degenerate eigenspaces to observable algebras defining generalized quantum subsystems. At fixed block structure, unitary invariance fixes a unique connection, recovering Berry--Wilczek--Zee transport on bands. On positive-dimensional strata, its holonomy is the special-unitary part of the normalizer: all inner logical gates and equal-type sector permutations are attainable. Given a compatible gapped Hamiltonian and access to the required paths, inner gates can be implemented adiabatically by isospectral control of a band refinement.
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BibTeX
@misc{zanardi2026universal,
title = {{Universal holonomic control of algebras of observables}},
author = {Paolo Zanardi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.28662},
eprint = {2609.28662},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28662},
}
RIS
TY - UNPB
TI - Universal holonomic control of algebras of observables
AU - Paolo Zanardi
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2609.28662
UR - https://arxiv.org/abs/2609.28662
AB - We extend geometric parallel transport from states and degenerate eigenspaces to observable algebras defining generalized quantum subsystems. At fixed block structure, unitary invariance fixes a unique connection, recovering Berry--Wilczek--Zee transport on bands. On positive-dimensional strata, its holonomy is the special-unitary part of the normalizer: all inner logical gates and equal-type sector permutations are attainable. Given a compatible gapped Hamiltonian and access to the required paths, inner gates can be implemented adiabatically by isospectral control of a band refinement.
ER -