Universal holonomic control of algebras of observables

Abstract:Closed paths of observable algebras can enact logical gates. We show that algebras of fixed block structure have a unique unitarily invariant parallel transport, recovering Berry--Wilczek--Zee transport on bands. On positive-dimensional configuration spaces, the holonomy group is the special-unitary part of the normalizer: every inner logical gate and every equal-type sector permutation is attainable. Given a compatible gapped Hamiltonian and access to the required paths, inner logical gates can be implemented adiabatically by isospectral control of a band refinement.

arXiv:2609.28662 [quant-ph]

(or arXiv:2609.28662v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.28662 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

hol-alg-sm-v3/README.md

hol-alg-sm-v3/algebra_types.py

hol-alg-sm-v3/based_curvature.py

hol-alg-sm-v3/common.py

hol-alg-sm-v3/manuscript-provenance.json

hol-alg-sm-v3/regression_controls.py

hol-alg-sm-v3/requirements.txt

hol-alg-sm-v3/results/algebra_types.json

hol-alg-sm-v3/results/algebra_types.log

hol-alg-sm-v3/results/based_curvature.json

hol-alg-sm-v3/results/based_curvature.log

hol-alg-sm-v3/results/manifest.json

hol-alg-sm-v3/results/regression_controls.json

hol-alg-sm-v3/results/regression_controls.log

hol-alg-sm-v3/results/sector_examples.json

hol-alg-sm-v3/results/sector_examples.log

hol-alg-sm-v3/results/tensor_topology.json

hol-alg-sm-v3/results/tensor_topology.log

hol-alg-sm-v3/results/transport.json

hol-alg-sm-v3/results/transport.log

hol-alg-sm-v3/run_checks.py

hol-alg-sm-v3/sector_examples.py

hol-alg-sm-v3/tensor_topology.py

hol-alg-sm-v3/transport.py

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