Fig. 3: Dynamics of stabilizers with random initial SPT states.
From: Digital quantum simulation of Floquet symmetry-protected topological phases
a, Schematic of the experimental circuit for preparing random SPT states. To prepare the system in the ground state of the stabilizer Hamiltonian Hs, we apply a Hadamard gate (H) on each qubit and then run CZ gates in parallel on all neighbouring qubit pairs in two steps. Then we apply Z operators on random sites to create excitations, thus transferring the ground state to a highly excited eigenstate of Hs. This procedure enables the preparation of random SPT states at high energy. We then evolve these states with the Hamiltonian H(t) to study the dynamics of stabilizers. b, Entanglement spectrum of a random SPT state evolved by one driving period, with open (left) and periodic (right) boundary conditions. The ‘Energy value index’ labels the eigenvalues of \(-\mathrm{ln}({\rho }_{{\rm{half}}})\). The red triangles with error bars are the experimental (Exp.) results and the grey dots show the numerical simulations (Sim.) that take into account experimental imperfections (Supplementary Information IV). The two- and four-fold degeneracy (in the case of open and periodic boundary conditions, respectively) of the low-lying entanglement levels is a characteristic feature of the topological nature of these states. c, The time dependence of stabilizers in the FSPT phase, averaged over 20 random circuit instances. The parameters in b and c are chosen as L = 10, δ = 0.1, J = Δj = 1, h = Δh = 0.01 and V = ΔV = 0.01.
