Classification of unitary operators by local generatability
Abstract
Periodically driven (Floquet) systems can exhibit possibilities beyond what can be obtained in equilibrium. Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic distinction arises among unitary time evolution operators: while all physical operators are local, not all are locally generated (i.e., generated by some local Hamiltonian). In this paper, we define the notion of equivalence up to a locally generated unitary in all Altland-Zirnbauer symmetry classes. We then classify noninteracting unitaries in all dimensions on this basis by showing that equivalence up to a locally generated unitary is identical to homotopy equivalence.
Cite
@article{arxiv.2308.02728,
title = {Classification of unitary operators by local generatability},
author = {Xu Liu and Adrian B. Culver and Fenner Harper and Rahul Roy},
journal= {arXiv preprint arXiv:2308.02728},
year = {2025}
}
Comments
15 + 9 pages, 2 figures; added Appendices A.2, B.1, and E; further discussion of composition operation; published version