
D. Vasilyev, A. Grankin, M. Baranov, L. Sieberer, P. Zoller Monitoring Quantum Simulators via Quantum NonDemolition Couplings to Atomic Clock Qubits,
PRX Quantum 1 (20201009),
http://dx.doi.org/10.1103/PRXQuantum.1.020302 doi:10.1103/PRXQuantum.1.020302 (ID: 720493)
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We discuss monitoring the time evolution of an analog quantum simulator via a quantum nondemolition (QND) coupling to an auxiliary `clock' qubit. The QND variable of interest is the `energy' of the quantum manybody system, represented by the Hamiltonian of the quantum simulator. We describe a physical implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in tweezer arrays using laser dressing schemes for a broad class of spin models. As an application, we discuss a quantum protocol for measuring the spectral form factor of quantum manybody systems, where the aim is to identify signatures of ergodic vs. nonergodic dynamics, which we illustrate for disordered 1D Heisenberg and Floquet spin models on Rydberg platforms. Our results also provide the physical ingredients for running quantum phase estimation protocols for measurement of energies, and preparation of energy eigenstates for a specified spectral resolution on an analog quantum simulator.

T. Olsacher, L. Postler, P. Schindler, T. Monz, P. Zoller, L. Sieberer Scalable and Parallel Tweezer Gates for Quantum Computing with Long Ion Strings,
PRX Quantum 1 20316 (20200826),
http://dx.doi.org/10.1103/PRXQuantum.1.020316 doi:10.1103/PRXQuantum.1.020316 (ID: 720527)
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Trappedion quantum computers have demonstrated highperformance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long onedimensional (1D) ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubitqubit couplings. Here, we devise methods to implement scalable and parallel entangling gates by using engineered localized phonon modes. We propose to tailor such localized modes by tuning the local potential of individual ions with programmable optical tweezers. Localized modes of small subsets of qubits form the basis to perform entangling gates on these subsets in parallel. We demonstrate the inherent scalability of this approach by presenting analytical and numerical results for long 1D ion chains and even for infinite chains of uniformly spaced ions. Furthermore, we show that combining our methods with optimal coherent control techniques allows to realize maximally dense universal parallelized quantum circuits.

A. Kruckenhauser, L. Sieberer, W. G. Tobias, K. Matsuda, L. De Marco, J. Li, G. Valtolina, A. M. Rey, J. Ye, M. Baranov, P. Zoller Quantum manybody physics with ultracold polar molecules: Nanostructured potential barriers and interactions,
Phys. Rev. A 102 23320 (20200819),
http://dx.doi.org/10.1103/PhysRevA.102.023320 doi:10.1103/PhysRevA.102.023320 (ID: 720474)
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We design dipolar quantum manybody Hamiltonians that will facilitate the realization of exotic quantum phases under current experimental conditions achieved for polar molecules. The main idea is to modulate both singlebody potential barriers and twobody dipolar interactions on a spatial scale of tens of nanometers to strongly enhance energy scales and, therefore, relax temperature requirements for observing new quantum phases of engineered manybody systems. We consider and compare two approaches. In the first, nanoscale barriers are generated with standingwave optical light fields exploiting optical nonlinearities. In the second, static electricfield gradients in combination with microwave dressing are used to write nanostructured spatial patterns on the induced electric dipole moments, and thus dipolar interactions. We study the formation of interlayer and interface bound states of molecules in these configurations, and provide detailed estimates for binding energies and expected losses for present experimental setups.

D. Yang, A. Grankin, L. Sieberer, D. Vasilyev, P. Zoller Quantum Nondemolition Measurement of a ManyBody Hamiltonian,
Nat. Commun. 11 (20200207),
http://dx.doi.org/10.1038/s41467020144895 doi:10.1038/s41467020144895 (ID: 720277)
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An ideal quantum measurement collapses the wave function of a quantum system to an eigenstate of the measured observable, with the corresponding eigenvalue determining the measurement outcome. For a quantum nondemolition (QND) observable, i.e., one that commutes with the Hamiltonian generating the system's time evolution, repeated measurements yield the same result, corresponding to measurements with minimal disturbance. This concept applies universally to single quantum particles as well as to complex manybody systems. However, while QND measurements of systems with few degrees of freedom has been achieved in seminal quantum optics experiments, it is an open challenge to devise QND measurement of a complex manybody observable. Here, we describe how a QND measurement of the Hamiltonian of an interacting manybody system can be implemented in a trappedion analog quantum simulator. Through a single shot measurement, the manybody system is prepared in a narrow energy band of (highly excited) energy eigenstates, and potentially even a single eigenstate. Our QND scheme, which can be carried over to other platforms of quantum simulation, provides a novel framework to investigate experimentally fundamental aspects of equilibrium and nonequilibrium statistical physics including the eigenstate thermalization hypothesis (ETH) and quantum fluctuation relations.

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 (20190920),
http://dx.doi.org/10.1038/s4153401901925 doi:10.1038/s4153401901925 (ID: 720105)
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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 trappedion quantum simulators which implement DQS of alltoall interacting spin1/2 systems. These platforms thus enable indepth studies of Trotter errors and their relation to signatures of quantum chaos, including the growth of outoftimeordered 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 (20190627),
http://dx.doi.org/10.1103/PhysRevX.9.021061 doi:10.1103/PhysRevX.9.021061 (ID: 720042)
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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 manybody systems. Our protocol, which does not require reversing time evolution or auxiliary degrees of freedom, can be realized in stateoftheart quantum simulation experiments.

C. Dlaska, L. Sieberer, W. Lechner Designing ground states of Hopfield networks for quantum state preparation,
Phys. Rev. A 99 (20190326),
http://dx.doi.org/10.1103/PhysRevA.99.032342 doi:10.1103/PhysRevA.99.032342 (ID: 720141)
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We present a protocol to store a polynomial number of arbitrary bit strings, encoded as spin configurations, in the approximately degenerate lowenergy manifold of an alltoall connected Ising spinglass. The iterative protocol is inspired by machine learning techniques utilizing klocal Hopfield networks trained with klocal Hebbian learning and unlearning. The trained Hamiltonian is the basis of a quantum state preparation scheme to create quantum manybody 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 klocality 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 (20181203),
http://dx.doi.org/10.1103/PhysRevB.98.214301 doi:10.1103/PhysRevB.98.214301 (ID: 720136)
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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 soughtafter 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 noiseaveraged 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 noiseinduced 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 (20180824),
http://dx.doi.org/10.1103/PhysRevLett.121.085704 doi:10.1103/PhysRevLett.121.085704 (ID: 720137)
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We study the dynamics and unbinding transition of vortices in the compact anisotropic KardarParisiZhang 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 vortexunbinding crossover in finitesize systems. These results are relevant for a wide variety of physical systems, ranging from strongly coupled lightmatter quantum systems to dissipative time crystals.

L. Sieberer, W. Lechner Programmable superpositions of Ising congurations,
Phys. Rev. A 97 (20180529),
http://dx.doi.org/10.1103/PhysRevA.97.052329 doi:10.1103/PhysRevA.97.052329 (ID: 720138)
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We present a framework to prepare superpositions of bit strings, i.e., manybody spin configurations, with deterministic programmable probabilities. The spin configurations are encoded in the degenerate ground states of the latticegauge representation of an alltoall connected Ising spin glass. The groundstate manifold is invariant under variations of the gauge degrees of freedom, which take the form of fourbody 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 (20180525),
http://dx.doi.org/10.1103/PhysRevLett.120.216801 doi:10.1103/PhysRevLett.120.216801 (ID: 720139)
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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, discretetime FloquetLindblad 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.