  Periodically driven (Floquet) systems can exhibit new 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 non-interacting unitaries in all dimensions on this basis by showing
that equivalence up to a locally generated unitary is identical to homotopy
equivalence.

Mesoscale and Nanoscale Physics;Quantum Gases;Strongly Correlated Electrons;Quantum Physics