Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Zanardi, Paolo
Institution: University of Southern California
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214338947