Publications Lukas SIEBERER

2022

Article

• T. Olsacher, L. Pastori, C. Kokail, L. Sieberer, Peter Zoller Digital quantum simulation, learning of the Floquet Hamiltonian, and quantum chaos of the kicked top, J. Phys. A: Math. Gen. 55 (2022-08-19), http://dx.doi.org/10.1088/1751-8121/ac8087 doi:10.1088/1751-8121/ac8087 (ID: 720859) Toggle Abstract
  The kicked top is one of the paradigmatic models in the study of quantum chaos (Haake et al 2018 Quantum Signatures of Chaos (Springer Series in Synergetics vol 54)). Recently it has been shown that the onset of quantum chaos in the kicked top can be related to the proliferation of Trotter errors in digital quantum simulation (DQS) of collective spin systems. Specifically, the proliferation of Trotter errors becomes manifest in expectation values of few-body observables strongly deviating from the target dynamics above a critical Trotter step, where the spectral statistics of the Floquet operator of the kicked top can be predicted by random matrix theory. In this work, we study these phenomena in the framework of Hamiltonian learning (HL). We show how a recently developed HL protocol can be employed to reconstruct the generator of the stroboscopic dynamics, i.e., the Floquet Hamiltonian, of the kicked top. We further show how the proliferation of Trotter errors is revealed by HL as the transition to a regime in which the dynamics cannot be approximately described by a low-order truncation of the Floquet–Magnus expansion. This opens up new experimental possibilities for the analysis of Trotter errors on the level of the generator of the implemented dynamics, that can be generalized to the DQS of quantum many-body systems in a scalable way. This paper is in memory of our colleague and friend Fritz Haake.

2021

Article

• S. S. Sayyad, J. Yu, A. G. Grushin, L. Sieberer Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology, Phys. Rev. Research 3 33022 (2021-07-06), http://dx.doi.org/10.1103/PhysRevResearch.3.033022 doi:10.1103/PhysRevResearch.3.033022 (ID: 720579) Toggle Abstract
  The development of non-Hermitian topological band theory has led to observations of novel topological phenomena in effectively classical, driven, and dissipative systems. However, for open quantum many-body systems, the absence of a ground state presents a challenge to define robust signatures of non-Hermitian topology. We show that such a signature is provided by crossings in the time evolution of the entanglement spectrum. These crossings occur in quenches from the trivial to the topological phase of a driven-dissipative Kitaev chain that is described by a Markovian quantum master equation in Lindblad form. At the topological transition, which can be crossed either by changing parameters of the Hamiltonian of the system or by increasing the strength of dissipation, the timescale at which the first entanglement spectrum crossing occurs diverges with a dynamical critical exponent of ε=1/2. We corroborate these numerical findings with an exact analytical solution of the quench dynamics for a spectrally flat postquench Liouvillian. This exact solution suggests an interpretation of the topological quench dynamics as a fermion parity pump. Our work thus reveals signatures of non-Hermitian topology that are unique to quantum many-body systems and cannot be emulated in classical simulators of non-Hermitian wave physics.

Preprint

• C. Kargi, J. P. Dehollain, F. Henriques, L. Sieberer, T. Olsacher, P. Hauke, M. Heyl, P. Zoller, N. Langford Quantum Chaos and Trotterisation Thresholds in Digital Quantum Simulations, (2021-10-21), arXiv:2110.11113 arXiv:2110.11113 (ID: 720694) Toggle Abstract
  Digital quantum simulation (DQS) is one of the most promising paths for achieving first useful real-world applications for quantum processors. Yet even assuming rapid progress in device engineering and development of fault-tolerant quantum processors, algorithmic resource optimisation will long remain crucial to exploit their full power. Currently, Trotterisation provides state-of-the-art DQS resource scaling. Moreover, recent theoretical studies of Trotterised Ising models suggest it also offers feasible performance for unexpectedly large step sizes up to a sharp breakdown threshold, but demonstrations and characterisation have been limited, and the question of whether this behaviour applies as a general principle has remained open. Here, we study a set of paradigmatic and experimentally realisable DQS models, and show that a range of Trotterisation performance behaviours, including the existence of a sharp threshold, are remarkably universal. Carrying out a detailed characterisation of a range of performance signatures, we demonstrate that it is the onset of digitisation-induced quantum chaos at this threshold that underlies the breakdown of Trotterisation. Specifically, combining analysis of detailed dynamics with conclusive, global static signatures based on random matrix theory, we observe clear signatures of regular behaviour pre-threshold, and conclusive, initial-state-independent evidence for the onset of quantum chaotic dynamics beyond the threshold. We also show how this behaviour consistently emerges as a function of system size for sizes and times already relevant for current experimental DQS platforms. The advances in this work open up many important questions about the algorithm performance and general shared features of sufficiently complex Trotterisation-based DQS. Answering these will be crucial for extracting the maximum simulation power from future quantum processors.

2020

Articles

• D. Vasilyev, A. Grankin, M. Baranov, L. Sieberer, P. Zoller Monitoring Quantum Simulators via Quantum Non-Demolition Couplings to Atomic Clock Qubits, PRX Quantum 1 (2020-10-09), http://dx.doi.org/10.1103/PRXQuantum.1.020302 doi:10.1103/PRXQuantum.1.020302 (ID: 720493) Toggle Abstract
  We discuss monitoring the time evolution of an analog quantum simulator via a quantum non-demolition (QND) coupling to an auxiliary `clock' qubit. The QND variable of interest is the `energy' of the quantum many-body 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 many-body systems, where the aim is to identify signatures of ergodic vs. non-ergodic 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 (2020-08-26), http://dx.doi.org/10.1103/PRXQuantum.1.020316 doi:10.1103/PRXQuantum.1.020316 (ID: 720527) Toggle Abstract
  Trapped-ion quantum computers have demonstrated high-performance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long one-dimensional (1D) ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubit-qubit 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 many-body physics with ultracold polar molecules: Nanostructured potential barriers and interactions, Phys. Rev. A 102 23320 (2020-08-19), http://dx.doi.org/10.1103/PhysRevA.102.023320 doi:10.1103/PhysRevA.102.023320 (ID: 720474) Toggle Abstract
  We design dipolar quantum many-body 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 single-body potential barriers and two-body 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 many-body systems. We consider and compare two approaches. In the first, nanoscale barriers are generated with standing-wave optical light fields exploiting optical nonlinearities. In the second, static electric-field 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 Non-demolition Measurement of a Many-Body Hamiltonian, Nat. Commun. 11 (2020-02-07), http://dx.doi.org/10.1038/s41467-020-14489-5 doi:10.1038/s41467-020-14489-5 (ID: 720277) Toggle Abstract
  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 non-demolition (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 many-body 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 many-body observable. Here, we describe how a QND measurement of the Hamiltonian of an interacting many-body system can be implemented in a trapped-ion analog quantum simulator. Through a single shot measurement, the many-body 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 non-equilibrium statistical physics including the eigenstate thermalization hypothesis (ETH) and quantum fluctuation relations.

2019

Articles

• 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) Toggle Abstract
  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) Toggle Abstract
  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) Toggle Abstract
  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.

2018

Articles

• 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) Toggle Abstract
  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) Toggle Abstract
  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) Toggle Abstract
  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) Toggle Abstract
  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.

2014

Article

• L. Sieberer, S. Huber, E. Altman, S. Diehl Non-equilibrium Functional Renormalization for Driven-Dissipative Bose-Einstein Condensation, Phys. Rev. B 89 134310 (2014-04-29), http://dx.doi.org/10.1103/PhysRevB.89.134310 doi:10.1103/PhysRevB.89.134310 (ID: 718617) Toggle Abstract
  We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. Starting point is a microscopic description of the system in terms of a many-body quantum master equation, where coherent and driven-dissipative dynamics occur on an equal footing. An equivalent Keldysh real time functional integral reformulation opens up the problem to a practical evaluation using the tools of quantum field theory. In particular, we develop a functional renormalization group approach to quantitatively explore the universality class of this stationary non-equilibrium system. Key results comprise the emergence of an asymptotic thermalization of the distribution function, while manifest non-equilibrium properties are witnessed in the response properties in terms of a new, independent critical exponent. Thus the driven-dissipative microscopic nature is seen to bear observable consequences on the largest length scales. The absence of two symmetries present in closed equilibrium systems - underlying particle number conservation and detailed balance, respectively - is identified as the root of this new non-equilibrium critical behavior. Our results are relevant for broad ranges of open quantum systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases.
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2013

Article

• L. Sieberer, S. Huber, E. Altman, S. Diehl Dynamical critical phenomena in driven-dissipative systems, Phys. Rev. Lett. 110 195301 (2013-05-07), http://dx.doi.org/10.1103/PhysRevLett.110.195301 doi:10.1103/PhysRevLett.110.195301 (ID: 718369) Toggle Abstract
  We explore the nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates. Using a functional renormalization group approach formulated in the Keldysh framework, we characterize the dynamical critical behavior that governs decoherence and an effective thermalization of the low frequency dynamics. We identify a critical exponent special to the driven system, showing that it defines a new dynamical universality class. Hence critical points in driven systems lie beyond the standard dynamical classification of equilibrium phase transitions. We show how the new critical exponent can be probed in experiments with driven cold atomic systems and exciton-polariton condensates.
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Preprint

• E. Altman, J. Toner, L. Sieberer, S. Diehl, L. Chen Two-dimensional superfluidity in driven systems requires strong anisotropy, (2013-11-04), arXiv:1311.0876 arXiv:1311.0876 (ID: 718667) Toggle Abstract
  We show that driven two-dimensional Bose systems cannot exhibit algebraic superfluid order unless the underlying microscopic system is strongly anisotropic. Our result implies, in particular, that recent apparent evidence for Bose condensation of exciton-polaritons in semiconductor quantum wells must be an intermediate scale crossover phenomenon, while the true long distance correlations fall off exponentially. We obtain these results through a mapping of the long-wavelength condensate dynamics onto the anisotropic Kardar-Parisi-Zhang equation.
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2011

Article

• L. Sieberer, M. Baranov Collective modes, stability, and superfluid transition of a quasi-two-dimensional dipolar Fermi gas, Phys. Rev. A 84 063633 (2011-12-22), http://dx.doi.org/10.1103/PhysRevA.84.063633 doi:10.1103/PhysRevA.84.063633 (ID: 717842) Toggle Abstract
  We examine collective modes, stability, and BCS pairing in a quasi-two-dimensional gas of dipolar fermions aligned by an external field. By using the (conserving) Hartree-Fock approximation, which treats direct and exchange interactions on an equal footing, we obtain the spectrum of single-particle excitations and long-wavelength collective modes (zero sound) in the normal phase. It appears that exchange interactions result in strong damping of zero sound when the tilting angle between the dipoles and the normal to the plane of confinement is below some critical value. In particular, zero sound cannot propagate if the dipoles are perpendicular to the plane of confinement. At intermediate coupling, we find unstable modes that can lead either to collapse of the system or to the formation of a density wave. The BCS transition to a superfluid phase, on the other hand, occurs at arbitrarily weak strengths of the dipole-dipole interaction, provided the tilting angle exceeds a critical value. We determine the critical temperature of the transition, taking into account many-body effects as well as virtual transitions to higher excited states in the confining potential, and discuss prospects of experimental observations.
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