25 research outputs found
Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topological chains
Much recent experimental effort has focused on the realization of exotic
quantum states and dynamics predicted to occur in periodically driven systems.
But how robust are the sought-after features, such as Floquet topological
surface states, against unavoidable imperfections in the periodic driving? In
this work, we address this question in a broader context and study the dynamics
of quantum systems subject to noise with periodically recurring statistics. We
show that the stroboscopic time evolution of such systems is described by a
noise-averaged Floquet superoperator. The eigenvectors and -values of this
superoperator generalize the familiar concepts of Floquet states and
quasienergies and allow us to describe decoherence due to noise efficiently.
Applying the general formalism to the example of a noisy Floquet topological
chain, we re-derive and corroborate our recent findings on the noise-induced
decay of topologically protected end states. These results follow directly from
an expansion of the end state in eigenvectors of the Floquet superoperator.Comment: 13 pages, 5 figures. This is the final, published versio
Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
This work aims at giving Trotter errors in digital quantum simulation (DQS)
of collective spin systems an interpretation in terms of quantum chaos of the
kicked top. In particular, for DQS of such systems, regular dynamics of the
kicked top ensures convergence of the Trotterized time evolution, while chaos
in the top, which sets in above a sharp threshold value of the Trotter step
size, corresponds to the proliferation of Trotter errors. We show the
possibility to analyze this phenomenology in a wide variety of experimental
realizations of the kicked top, ranging from single atomic spins to trapped-ion
quantum simulators which implement DQS of all-to-all interacting spin-1/2
systems. These platforms thus enable in-depth studies of Trotter errors and
their relation to signatures of quantum chaos, including the growth of
out-of-time-ordered correlators.Comment: 20 pages, 6 figure