L. Sieberer, T. Olsacher, A. Elben, M. Heyl, P. Hauke, F. Haake, P. Zoller Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top,
npj Quantum Information 5 (2019-09-20),
http://dx.doi.org/10.1038/s41534-019-0192-5 doi:10.1038/s41534-019-0192-5 (ID: 720105)
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.
B. Vermersch, A. Elben, L. Sieberer, N. Y. Yao, P. Zoller Probing scrambling using statistical correlations between randomized measurements,
Phys. Rev. X 9 21061 (2019-06-27),
http://dx.doi.org/10.1103/PhysRevX.9.021061 doi:10.1103/PhysRevX.9.021061 (ID: 720042)
We present a protocol to study scrambling using statistical correlations between measurements, performed after evolving a quantum system from random initial states. We show that the resulting statistical correlations are directly related to OTOCs and can be used to probe scrambling in many-body systems. Our protocol, which does not require reversing time evolution or auxiliary degrees of freedom, can be realized in state-of-the-art quantum simulation experiments.
C. Dlaska, L. Sieberer, W. Lechner Designing ground states of Hopfield networks for quantum state preparation,
Phys. Rev. A 99 (2019-03-26),
http://dx.doi.org/10.1103/PhysRevA.99.032342 doi:10.1103/PhysRevA.99.032342 (ID: 720141)
We present a protocol to store a polynomial number of arbitrary bit strings, encoded as spin configurations, in the approximately degenerate low-energy manifold of an all-to-all connected Ising spin-glass. The iterative protocol is inspired by machine learning techniques utilizing k-local Hopfield networks trained with k-local Hebbian learning and unlearning. The trained Hamiltonian is the basis of a quantum state preparation scheme to create quantum many-body superpositions with tunable squared amplitudes using resources available in near term experiments. We find that the number of configurations that can be stored in the ground states, and thus turned into superposition, scales with the k-locality of the Ising interaction.
L. Sieberer, M. T. Rieder, M. H. Fischer, I. C. Fulga Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topological chains,
Phys. Rev. B 98 (2018-12-03),
http://dx.doi.org/10.1103/PhysRevB.98.214301 doi:10.1103/PhysRevB.98.214301 (ID: 720136)
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 paper, 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 rederive 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.
L. Sieberer, E. Altman Topological Defects in Anisotropic Driven Open Systems,
Phys. Rev. Lett. 121 (2018-08-24),
http://dx.doi.org/10.1103/PhysRevLett.121.085704 doi:10.1103/PhysRevLett.121.085704 (ID: 720137)
We study the dynamics and unbinding transition of vortices in the compact anisotropic Kardar-Parisi-Zhang equation. The combination of nonequilibrium conditions and strong spatial anisotropy drastically affects the structure of vortices and amplifies their mutual binding forces, thus stabilizing the ordered phase. We find novel universal critical behavior in the vortex-unbinding crossover in finite-size systems. These results are relevant for a wide variety of physical systems, ranging from strongly coupled light-matter quantum systems to dissipative time crystals.
L. Sieberer, W. Lechner Programmable superpositions of Ising congurations,
Phys. Rev. A 97 (2018-05-29),
http://dx.doi.org/10.1103/PhysRevA.97.052329 doi:10.1103/PhysRevA.97.052329 (ID: 720138)
We present a framework to prepare superpositions of bit strings, i.e., many-body spin configurations, with deterministic programmable probabilities. The spin configurations are encoded in the degenerate ground states of the lattice-gauge representation of an all-to-all connected Ising spin glass. The ground-state manifold is invariant under variations of the gauge degrees of freedom, which take the form of four-body parity constraints. Our framework makes use of these degrees of freedom by individually tuning them to dynamically prepare programmable superpositions. The dynamics combines an adiabatic protocol with controlled diabatic transitions. We derive an effective model that allows one to determine the control parameters efficiently even for large system sizes.
M. T. Rieder, L. Sieberer, M. H. Fischer, I. C. Fulga Localization Counteracts Decoherence in Noisy Floquet Topological Chains,
Phys. Rev. Lett. 120 (2018-05-25),
http://dx.doi.org/10.1103/PhysRevLett.120.216801 doi:10.1103/PhysRevLett.120.216801 (ID: 720139)
The topological phases of periodically driven, or Floquet systems, rely on a perfectly periodic modulation of system parameters in time. Even the smallest deviation from periodicity leads to decoherence, causing the boundary (end) states to leak into the system’s bulk. Here, we show that in one dimension this decay of topologically protected end states depends fundamentally on the nature of the bulk states: a dispersive bulk results in an exponential decay, while a localized bulk slows the decay down to a diffusive process. The localization can be due to disorder, which remarkably counteracts decoherence even when it breaks the symmetry responsible for the topological protection. We derive this result analytically, using a novel, discrete-time Floquet-Lindblad formalism and confirm our findings with the help of numerical simulations. Our results are particularly relevant for experiments, where disorder can be tailored to protect Floquet topological phases from decoherence.