Publications Benoit VERMERSCH

2023

Preprint

• D. González-Cuadra, D. Bluvstein, M. Kalinowski, C. R. Kaubrügger, N. Maskara, P. Naldesi, T. Zache, A. Kaufman, M. Lukin, H. Pichler, B. Vermersch, J. Ye, P. Zoller Fermionic quantum processing with programmable neutral atom arrays, (2023-03-13), arXiv:2303.06985 arXiv:2303.06985 (ID: 721066) Toggle Abstract
  Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding non-local fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement non-local tunneling gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation, as well as to simulate lattice gauge theory dynamics.

2022

Articles

• A. Elben, S. Flammia, Hsin Y. Huang, R. Kueng, J. Preskill, B. Vermersch, Peter Zoller The randomized measurement toolbox, Nat. Rev. Phys. s42254 (2022-12-02), http://dx.doi.org/10.1038/s42254-022-00535-2 doi:10.1038/s42254-022-00535-2 (ID: 720824) Toggle Abstract
  Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large quantum systems is the source of their power, but also makes them difficult to control precisely or characterize accurately using measured classical data. We review recently developed protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms. In all these protocols, a quantum state is repeatedly prepared and measured in a randomly chosen basis; then a classical computer processes the measurement outcomes to estimate the desired property. The randomization of the measurement procedure has distinct advantages; for example, a single data set can be employed multiple times to pursue a variety of applications, and imperfections in the measurements are mapped to a simplified noise model that can more easily be mitigated. We discuss a range of use cases that have already been realized in quantum devices, including Hamiltonian simulation tasks, probes of quantum chaos, measurements of nonlocal order parameters, and comparison of quantum states produced in distantly separated laboratories. By providing a workable method for translating a complex quantum state into a succinct classical representation that preserves a rich variety of relevant physical properties, the randomized measurement toolbox strengthens our ability to grasp and control the quantum world.
• M. Dalmonte, Viktor Eisler, Marco Falconi, B. Vermersch Entanglement Hamiltonians: From Field Theory to Lattice Models and Experiments, Ann. Phys. 2022 (2022-08-17), http://dx.doi.org/10.1002/andp.202200064 doi:10.1002/andp.202200064 (ID: 721053) Toggle Abstract
  Results about entanglement (or modular) Hamiltonians of quantum many-body systems in field theory and statistical mechanics models, and recent applications in the context of quantum information and quantum simulation, are reviewed. In the first part of the review, what is known about entanglement Hamiltonians of ground states (vacua) in quantum field theory is summarized, based on the Bisognano–Wichmann theorem and its extension to conformal field theory. This is complemented with a more rigorous mathematical discussion of the Bisognano–Wichmann theorem, within the framework of Tomita–Takesaki theorem of modular groups. The second part of the review is devoted to lattice models. There, exactly soluble cases are first considered and then the discussion is extended to non-integrable models, whose entanglement Hamiltonian is often well captured by the lattice version of the Bisognano–Wichmann theorem. In the last part of the review, recently developed applications in quantum information processing that rely upon the specific properties of entanglement Hamiltonians in many-body systems are summarized. These include protocols to measure entanglement spectra, and schemes to perform state tomography.
• V. Vitale, A. Elben, R. Kueng, A. Neven, J. Carrasco, Barbara Kraus, Peter Zoller, P. Calabrese, B. Vermersch, M. Dalmonte Symmetry-resolved dynamical purification in synthetic quantum matter, SciPost Phys. 12 106 (2022-03-25), http://dx.doi.org/10.21468/SciPostPhys.12.3.106 doi:10.21468/SciPostPhys.12.3.106 (ID: 720887) Toggle Abstract
  Abstract<br /> <br /> When a quantum system initialized in a product state is subjected to either coherent or incoherent dynamics, the entropy of any of its connected partitions generically increases as a function of time, signalling the inevitable spreading of (quantum) information throughout the system. Here, we show that, in the presence of continuous symmetries and under ubiquitous experimental conditions, symmetry-resolved information spreading is inhibited due to the competition of coherent and incoherent dynamics: in given quantum number sectors, entropy decreases as a function of time, signalling dynamical purification. Such dynamical purification bridges between two distinct short and intermediate time regimes, characterized by a log-volume and log-area entropy law, respectively. It is generic to symmetric quantum evolution, and as such occurs for different partition geometry and topology, and classes of (local) Liouville dynamics. We then develop a protocol to measure symmetry-resolved entropies and negativities in synthetic quantum systems based on the random unitary toolbox, and demonstrate the generality of dynamical purification using experimental data from trapped ion experiments [Brydges et al., Science 364, 260 (2019)]. Our work shows that symmetry plays a key role as a magnifying glass to characterize many-body dynamics in open quantum systems, and, in particular, in noisy-intermediate scale quantum devices.
• L. K. Joshi, A. Elben, A. Vikram, B. Vermersch, V. Galitski, P. Zoller Probing many-body quantum chaos with quantum simulators, Phys. Rev. X (2022-01-27), http://dx.doi.org/10.1103/PhysRevX.12.011018 doi:10.1103/PhysRevX.12.011018 (ID: 720665) Toggle Abstract
  The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (pSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol which allows the measurement of SFF and pSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified testbed to probe many-body quantum chaotic behavior, thermalization and many-body localization in closed quantum systems which we illustrate with simulations for Hamiltonian and Floquet many-body spin-systems.

Preprints

• J. Carrasco, M. Votto, V. Vitale, C. Kokail, A. Neven, Peter Zoller, B. Vermersch, Barbara Kraus Entanglement phase diagrams from partial transpose moments, (2022-12-20), arXiv:2212.10181 arXiv:2212.10181 (ID: 720958) Toggle Abstract
  We present experimentally and numerically accessible quantities that can be used to differentiate among various families of random entangled states. To this end, we analyze the entanglement properties of bipartite reduced states of a tripartite pure state. We introduce a ratio of simple polynomials of low-order moments of the partially transposed reduced density matrix and show that this ratio takes well-defined values in the thermodynamic limit for various families of entangled states. This allows to sharply distinguish entanglement phases, in a way that can be understood from a quantum information perspective based on the spectrum of the partially transposed density matrix. We analyze in particular the entanglement phase diagram of Haar random states, states resulting form the evolution of chaotic Hamiltonians, stabilizer states, which are outputs of Clifford circuits, Matrix Product States, and fermionic Gaussian states. We show that for Haar random states the resulting phase diagram resembles the one obtained via the negativity and that for all the cases mentioned above a very distinctive behaviour is observed. Our results can be used to experimentally test necessary conditions for different types of mixed-state randomness, in quantum states formed in quantum computers and programmable quantum simulators.
• P. Naldesi, A. Elben, A. Minguzzi, D. Clement, Peter Zoller, B. Vermersch Fermionic correlation functions from randomized measurements in programmable atomic quantum devices, (2022-05-02), arXiv:2205.00981 arXiv:2205.00981 (ID: 720886) Toggle Abstract
  We provide a measurement protocol to estimate 2- and 4-point fermionic correlations in ultra-cold atom experiments. Our approach is based on combining random atomic beam splitter operations, which can be realized with programmable optical landscapes, with high-resolution imaging systems such as quantum gas microscopes. We illustrate our results in the context of the variational quantum eigensolver algorithm for solving quantum chemistry problems.

2021

Articles

• A. Rath, R. van Bijnen, A. Elben, P. Zoller, B. Vermersch Importance sampling of randomized measurements for probing entanglement, Phys. Rev. Lett. 127 (2021-11-11), http://dx.doi.org/10.1103/PhysRevLett.127.200503 doi:10.1103/PhysRevLett.127.200503 (ID: 720632) Toggle Abstract
  We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of statistical errors is obtained using classical techniques of machine-learning and tensor networks using partial information on the quantum state. In present experimental settings of engineered many-body quantum systems this effectively doubles the (sub-)system sizes for which entanglement can be measured. In particular, we show an exponential reduction of the required number of measurements to estimate the purity of product states and GHZ states.
• C. Kokail, B. Sundar, T. Zache, A. Elben, B. Vermersch, M. Dalmonte, R. van Bijnen, P. Zoller Quantum Variational Learning of the Entanglement Hamiltonian, Phys. Rev. Lett. 127 170501 (2021-10-22), http://dx.doi.org/10.1103/PhysRevLett.127.170501 doi:10.1103/PhysRevLett.127.170501 (ID: 720649) Toggle Abstract
  Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.
• A. Neven, J. Carrasco, V. Vitale, C. Kokail, A. Elben, M. Dalmonte, P. Calabrese, P. Zoller, B. Vermersch, R. Kueng, B. Kraus Symmetry-resolved entanglement detection using partial transpose moments, npj Quantum Information 7 (2021-10-20), http://dx.doi.org/10.1038/s41534-021-00487-y doi:10.1038/s41534-021-00487-y (ID: 720635) Toggle Abstract
  We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The k-th condition involves comparing moments of the partially transposed density operator up to order k. Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.
• C. Kokail, R. van Bijnen, A. Elben, B. Vermersch, P. Zoller Entanglement Hamiltonian Tomography in Quantum Simulation, Nature Phys. (2021-06-24), http://dx.doi.org/10.1038/s41567-021-01260-w doi:10.1038/s41567-021-01260-w (ID: 720530) Toggle Abstract
  Entanglement is the crucial ingredient of quantum many-body physics, and characterizing and quantifying entanglement in closed system dynamics of quantum simulators is an outstanding challenge in today's era of intermediate scale quantum devices. Here we discuss an efficient tomographic protocol for reconstructing reduced density matrices and entanglement spectra for spin systems. The key step is a parametrization of the reduced density matrix in terms of an entanglement Hamiltonian involving only quasi local few-body terms. This ansatz is fitted to, and can be independently verified from, a small number of randomised measurements. The ansatz is suggested by Conformal Field Theory in quench dynamics, and via the Bisognano-Wichmann theorem for ground states. Not only does the protocol provide a testbed for these theories in quantum simulators, it is also applicable outside these regimes. We show the validity and efficiency of the protocol for a long-range Ising model in 1D using numerical simulations. Furthermore, by analyzing data from 10 and 20 ion quantum simulators [Brydges \textit{et al.}, Science, 2019], we demonstrate measurement of the evolution of the entanglement spectrum in quench dynamics.
• V. Vitale, A. Elben, R. Kueng, A. Neven, J. Carrasco, B. Kraus, P. Zoller, P. Calabrese, B. Vermersch, M. Dalmonte Symmetry-resolved dynamical purification in synthetic quantum matter, SciPost Phys. 12 (2021-03-25), http://dx.doi.org/10.21468/SciPostPhys.12.3.106 doi:10.21468/SciPostPhys.12.3.106 (ID: 720620)
• Z. Cian, H. Dehghani, A. Elben, B. Vermersch, G. Zhu, M. Barkeshli, P. Zoller, M. Hafezi Many-body Chern number from statistical correlations of randomized measurements, Phys. Rev. Lett. 126 50501 (2021-02-01), http://dx.doi.org/10.1103/PhysRevLett.126.050501 doi:10.1103/PhysRevLett.126.050501 (ID: 720496) Toggle Abstract
  One of the main topological invariants that characterizes several topologically-ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant is conventionally based on the linear-response techniques which require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators. Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wavefunction. Remarkably, our results apply to disk-like geometries that are more amenable to current quantum simulator architectures.

2020

Articles

• A. Elben, R. Kueng, H. Huang, R. van Bijnen, C. Kokail, M. Dalmonte, P. Calabrese, B. Kraus, J. Preskill, P. Zoller, B. Vermersch Mixed-state entanglement from local randomized measurements, Phys. Rev. Lett. 125 (2020-11-11), http://dx.doi.org/10.1103/PhysRevLett.125.200501 doi:10.1103/PhysRevLett.125.200501 (ID: 720525) Toggle Abstract
  We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state, followed by post-processing using the classical shadows framework. Our method can be applied to any quantum system with single-qubit control. We provide a detailed analysis of the required number of experimental runs, and demonstrate the protocol using existing experimental data [Brydges et al, Science 364, 260 (2019)].
• A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. Lukin, P. Zoller Emerging 2D Gauge theories in Rydberg configurable arrays, Phys. Rev. X 10 (2020-06-16), http://dx.doi.org/10.1103/PhysRevX.10.021057 doi:10.1103/PhysRevX.10.021057 (ID: 720355) Toggle Abstract
  Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter. On a lattice, gauge invariance and gauge invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize. Here we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian --a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics. Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade. Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs. We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically, and probe them and their quench dynamics by on-site measurements of their quantum correlations. We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.
• A. Elben, J. Yu, G. Zhu, M. Hafezi, F. Pollmann, P. Zoller, B. Vermersch Many-body topological invariants from randomized measurements, Sci. Adv. 6 (2020-04-10), http://dx.doi.org/10.1126/sciadv.aaz3666 doi:10.1126/sciadv.aaz3666 (ID: 720289) Toggle Abstract
  The classification of symmetry-protected topological (SPT) phases in one dimension has been recently achieved, and had a fundamental impact in our understanding of quantum phases in condensed matter physics. In this framework, SPT phases can be identified by many-body topological invariants, which are quantized non-local correlators for the many-body wavefunction. While SPT phases can now be realized in interacting synthethic quantum systems, the direct measurement of quantized many-body topological invariants has remained so far elusive. Here, we propose measurement protocols for many-body topological invariants for all types of protecting symmetries of one-dimensional interacting bosonic systems. Our approach relies on randomized measurements implemented with local random unitaries, and can be applied to any spin system with single-site addressability and readout. Our scheme thus provides a versatile toolbox to experimentally classify interacting SPT phases.
• P. Guimond, B. Vermersch, M. L. Juan, A. Sharafiev, G. Kirchmair, P. Zoller A Unidirectional On-Chip Photonic Interface for Superconducting Circuits, npj Quantum Information 6 (2020-03-27), http://dx.doi.org/10.1038/s41534-020-0261-9 doi:10.1038/s41534-020-0261-9 (ID: 720478) Toggle Abstract
  We propose and analyze a passive architecture for realizing on-chip, scalable cascaded quantum devices. In contrast to standard approaches, our scheme does not rely on breaking Lorentz reciprocity. Rather, we engineer the interplay between pairs of superconducting transmon qubits and a microwave transmission line, in such a way that two delocalized orthogonal excitations emit (and absorb) photons propagating in opposite directions. We show how such cascaded quantum devices can be exploited to passively probe and measure complex many-body operators on quantum registers of stationary qubits, thus enabling the heralded transfer of quantum states between distant qubits, as well as the generation and manipulation of stabilizer codes for quantum error correction.
• M. K. Joshi, A. Elben, B. Vermersch, T. Brydges, C. Maier, P. Zoller, R. Blatt, C. F. Roos Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions, Phys. Rev. Lett. 124 240505 (2020-01-07), http://dx.doi.org/10.1103/PhysRevLett.124.240505 doi:10.1103/PhysRevLett.124.240505 (ID: 720436) Toggle Abstract
  In ergodic many-body quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling" is currently of intense research interest, entailing a deep understanding of many-body dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10-qubit trapped-ion quantum simulator representing a tunable long-range interacting spin system, by estimating out-of-time ordered correlators (OTOCs) through randomized measurements. We also analyze the role of decoherence in our system by comparing our measurements to numerical simulations and by measuring Rényi entanglement entropies.
• A. Elben, B. Vermersch, R. van Bijnen, C. Kokail, T. Brydges, C. Maier, M. K. Joshi, R. Blatt, C. F. Roos, P. Zoller Cross-Platform Verification of Intermediate Scale Quantum Devices, Phys. Rev. Lett. 124 10504 (2020-01-06), http://dx.doi.org/10.1103/PhysRevLett.124.010504 doi:10.1103/PhysRevLett.124.010504 (ID: 720357) Toggle Abstract
  We describe a protocol for cross-platform verification of quantum simulators and quantum computers. We show how to measure directly the overlap Tr[ρ1ρ2] and the purities Tr[ρ21,2], and thus a (mixed-state) fidelity, of two quantum states ρ1 and ρ2 prepared in separate experimental platforms. We require only local measurements in randomized product bases, which are communicated classically. As a proof-of-principle, we present the measurement of experiment-theory fidelities for entangled 10-qubit quantum states in a trapped ion quantum simulator.

2019

Articles

• M. Schütz, B. Vermersch, G. Kirchmair, L. Vandersypen, J. I. Cirac, M. Lukin, P. Zoller Quantum Simulation and Optimization in Hot Quantum Networks, Phys. Rev. B 99 241302 (2019-06-27), http://dx.doi.org/10.1103/PhysRevB.99.241302 doi:10.1103/PhysRevB.99.241302 (ID: 720058) Toggle Abstract
  We propose and analyze a setup based on (solid-state) qubits coupled to a common multi-mode transmission line, which allows for coherent spin-spin interactions over macroscopic on-chip distances, without any ground-state cooling requirements for the data bus. Our approach allows for the realization of fast deterministic quantum gates between distant qubits, the simulation of quantum spin models with engineered (long-range) interactions, and provides a flexible architecture for the implementation of quantum approximate optimization algorithms.
• 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.
• A. Elben, B. Vermersch, C. F. Roos, P. Zoller Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states, Phys. Rev. A 99 52323 (2019-05-15), http://dx.doi.org/10.1103/PhysRevA.99.052323 doi:10.1103/PhysRevA.99.052323 (ID: 720100) Toggle Abstract
  We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second Rényi entropy of highly mixed quantum states consisting of up to 10 qubits in a trapped-ion quantum simulator [Brydges et al., arXiv:1806.05747]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in an experiment. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.
• T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, C. F. Roos Probing Renyi entanglement entropy via randomized measurements, Science 364 260 (2019-04-19), http://dx.doi.org/10.1126/science.aau4963 doi:10.1126/science.aau4963 (ID: 720034) Toggle Abstract
  Entanglement is the key feature of many-body quantum systems, and the development of new tools to probe it in the laboratory is an outstanding challenge. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a new protocol for measuring entropy, based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts - both in the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, applicable to arbitrary quantum states of up to several tens of qubits.
• P. Guimond, A. Grankin, D. Vasilyev, B. Vermersch, P. Zoller Subradiant Bell States in Distant Atomic Arrays, Phys. Rev. Lett. 122 93601 (2019-03-05), http://dx.doi.org/10.1103/PhysRevLett.122.093601 doi:10.1103/PhysRevLett.122.093601 (ID: 720126) Toggle Abstract
  We study collective “free-space” radiation properties of two distant single-layer arrays of quantum emitters as two-level atoms. We show that this system can support a long-lived Bell superposition state of atomic excitations exhibiting strong subradiance, which corresponds to a nonlocal excitation of the two arrays. We describe the preparation of these states and their application in quantum information as a resource of nonlocal entanglement, including deterministic quantum state transfer with high fidelity between the arrays representing quantum memories. We discuss experimental realizations using cold atoms in optical trap arrays with subwavelength spacing, and analyze the role of imperfections.

2018

Articles

• A. Grankin, D. Vasilyev, P. Guimond, B. Vermersch, P. Zoller Free-space photonic quantum link and chiral quantum optics, Phys. Rev. A 98 3825 (2018-10-12), http://dx.doi.org/10.1103/PhysRevA.98.043825 doi:10.1103/PhysRevA.98.043825 (ID: 719980) Toggle Abstract
  We present the design of a chiral photonic quantum link, where distant atoms interact by exchanging photons propagating in a single direction in free space. This is achieved by coupling each atom in a laser-assisted process to an atomic array acting as a quantum phased-array antenna. This provides a basic building block for quantum networks in free space, i.e., without requiring cavities or nanostructures, which we illustrate with high-fidelity quantum state transfer protocols. Our setup can be implemented with neutral atoms using Rydberg-dressed interactions.
• M. Dalmonte, B. Vermersch, P. Zoller Quantum simulation and spectroscopy of entanglement Hamiltonians, Nature Phys. 14 151 (2018-05-21), http://dx.doi.org/10.1038/s41567-018-0151-7 doi:10.1038/s41567-018-0151-7 (ID: 720028) Toggle Abstract
  The properties of a strongly correlated many-body quantum system, from the presence of topological order to the onset of quantum criticality, leave a footprint in its entanglement spectrum. The entanglement spectrum is composed by the eigenvalues of the density matrix representing a subsystem of the whole original system, but its direct measurement has remained elusive due to the lack of direct experimental probes. Here we show that the entanglement spectrum of the ground state of a broad class of Hamiltonians becomes directly accessible via the quantum simulation and spectroscopy of a suitably constructed entanglement Hamiltonian, building on the Bisognano–Wichmann theorem of axiomatic quantum field theory. This theorem gives an explicit physical construction of the entanglement Hamiltonian, identified as the Hamiltonian of the many-body system of interest with spatially varying couplings. On this basis, we propose a scalable recipe for the measurement of a system’s entanglement spectrum via spectroscopy of the corresponding Bisognano–Wichmann Hamiltonian realized in synthetic quantum systems, including atoms in optical lattices and trapped ions. We illustrate and benchmark this scenario on a variety of models, spanning phenomena as diverse as conformal field theories, topological order and quantum phase transitions.
• B. Vermersch, A. Elben, M. Dalmonte, J. I. Cirac, P. Zoller Unitary n-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies, Phys. Rev. A 97 23604 (2018-02-02), http://dx.doi.org/10.1103/PhysRevA.97.023604 doi:10.1103/PhysRevA.97.023604 (ID: 719928) Toggle Abstract
  We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary n-designs, and their application to the measurement of R\'enyi entropies. We generalize our protocol presented in [Elben2017: arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and spin lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum chaos.
  (local copy)
• A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, P. Zoller Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models, Phys. Rev. Lett. 120 50406 (2018-02-02), http://dx.doi.org/10.1103/PhysRevLett.120.050406 doi:10.1103/PhysRevLett.120.050406 (ID: 719876) Toggle Abstract
  We present a scheme for measuring Rényi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimension. Our approach is based on the generation of random unitaries from random quenches, implemented using engineered time-dependent disorder potentials, and standard projective measurements, as realized by quantum gas microscopes. By analyzing the properties of the generated unitaries and the role of statistical errors, with respect to the size of the partition, we show that the protocol can be realized in exisiting AMO quantum simulators, and used to measure for instance area law scaling of entanglement in two-dimensional spin models or the entanglement growth in many-body localized systems.
  (local copy)

2017

Articles

• B. Vogell, B. Vermersch, T. E. Northup, B. P. Lanyon, C. A. Muschik Deterministic quantum state transfer between remote qubits in cavities, Quantum Sci. Technol. 2 45003 (2017-09-08), http://dx.doi.org/10.1088/2058-9565/aa868b doi:10.1088/2058-9565/aa868b (ID: 719794) Toggle Abstract
  Performing a faithful transfer of an unknown quantum state is a key challenge for enabling quantum networks. The realization of networks with a small number of quantum links is now actively pursued, which calls for an assessment of different state transfer methods to guide future design decisions. Here, we theoretically investigate quantum state transfer between two distant qubits, each in a cavity, connected by a waveguide, e.g., an optical fiber. We evaluate the achievable state transfer fidelities for two different protocols: standard wave packet shaping and adiabatic passage. The main loss sources are transmission losses in the waveguide and absorption losses in the cavities. While special cases studied in the literature indicate that adiabatic passages may be beneficial in this context, it remained an open question under which conditions this is the case and whether their use will be advantageous in practice. We answer these questions by providing a full analysis, showing that state transfer by adiabatic passage -- in contrast to wave packet shaping -- can mitigate the effects of undesired cavity losses, far beyond the regime of coupling to a single waveguide mode and the regime of lossless waveguides, as was proposed so far. We also clarify that neither protocol can avoid losses in the waveguide and discuss how the cavity parameters should be chosen.
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• A. Mazloom Shahraki, B. Vermersch, M. Baranov, M. Dalmonte Adiabatic state preparation of stripe phases with strongly magnetic atoms, Phys. Rev. A 96 33602 (2017-09-01), http://dx.doi.org/10.1103/PhysRevA.96.033602 doi:10.1103/PhysRevA.96.033602 (ID: 719755) Toggle Abstract
  We propose a protocol for realizing the stripe phase in two spin models on a two-dimensional square lattice, which can be implemented with strongly magnetic atoms (Cr, Dy, Er, etc.) in optical lattices by encoding spin states into Zeeman sublevels of the ground state manifold. The protocol is tested with cluster-mean-field time-dependent variational ans\"atze, validated by comparison with exact results for small systems, which enable us to simulate the dynamics of systems with up to 64 sites during the state-preparation protocol. This allows, in particular, to estimate the time required for preparation of the stripe phase with high fidelity under real experimental conditions.
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• B. Vermersch, P. Guimond, H. Pichler, P. Zoller Quantum State Transfer via Noisy Photonic and Phononic Waveguides, Phys. Rev. Lett. 118 133601 (2017-03-27), http://dx.doi.org/10.1103/PhysRevLett.118.133601 doi:10.1103/PhysRevLett.118.133601 (ID: 719696) Toggle Abstract
  We describe a quantum state transfer protocol, where a quantum state of photons stored in a first cavity can be faithfully transferred to a second distant cavity via an infinite 1D waveguide, while being immune to arbitrary noise (e.g. thermal noise) injected into the waveguide. We extend the model and protocol to a cavity QED setup, where atomic ensembles, or single atoms representing quantum memory, are coupled to a cavity mode. We present a detailed study of sensitivity to imperfections, and develop a quantum error correction protocol to account for random losses (or additions) of photons in the waveguide. Our numerical analysis is enabled by Matrix Product State techniques to simulate the complete quantum circuit, which we generalize to include thermal input fields. Our discussion applies both to photonic and phononic quantum networks.
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• C. Dlaska, B. Vermersch, P. Zoller Robust quantum state transfer via topologically protected edge channels in dipolar arrays, Quantum Sci. Technol. 2 15001 (2017-01-05), http://dx.doi.org/10.1088/2058-9565/2/1/015001 doi:10.1088/2058-9565/2/1/015001 (ID: 719597) Toggle Abstract
  We show how to realize quantum state transfer between distant qubits using the chiral edge states of a two-dimensional topological spin system. Our implementation based on Rydberg atoms allows to realize the quantum state transfer protocol in state of the art experimental setups. In particular, we show how to adapt the standard state transfer protocol to make it robust against dispersive and disorder effects.
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2016

Articles

• B. Vermersch, T. Ramos, P. Hauke, P. Zoller Implementation of Chiral Quantum Optics with Rydberg and Trapped-ion Setups, Phys. Rev. A 93 63830 (2016-06-17), http://dx.doi.org/10.1103/PhysRevA.93.063830 doi:10.1103/PhysRevA.93.063830 (ID: 719538) Toggle Abstract
  We propose two setups for realizing a chiral quantum network, where two-level systems representing the nodes interact via directional emission into discrete waveguides, as introduced in Ref.~[T.\ Ramos \emph{et al.}, arXiv:1602.00926]. The first implementation realizes a spin waveguide via Rydberg states in a chain of atoms, whereas the second one realizes a phonon waveguide via the localized vibrations of a string of trapped ions. For both architectures, we show that strong chirality can be obtained by a proper design of synthetic gauge fields in the couplings from the nodes to the waveguide. In the Rydberg case, this is achieved via intrinsic spin-orbit coupling in the dipole-dipole interactions, while for the trapped ions it is obtained by engineered sideband transitions. We take long-range couplings into account that appear naturally in these implementations, discuss useful experimental parameters, and analyze potential error sources. Finally, we describe effects that can be observed in these implementations within state-of-the-art technology, such as the driven-dissipative formation of entangled dimer states.
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• T. Ramos, B. Vermersch, P. Hauke, H. Pichler, P. Zoller Non-Markovian Dynamics in Chiral Quantum Networks with Spins and Photons, Phys. Rev. A 93 62104 (2016-06-02), http://dx.doi.org/10.1103/PhysRevA.93.062104 doi:10.1103/PhysRevA.93.062104 (ID: 719497) Toggle Abstract
  We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to the familiar photonic networks consisting of driven two-level atoms exchanging photons via 1D photonic nanostructures, we propose and study a setup where interactions between the atoms are mediated by spin excitations (magnons) in 1D XX-spin chains representing a spin waveguide. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a Born-Markov approximation to obtain a master equation for the nodes, we are interested in non-Markovian dynamics. This arises from the nonlinear character of the dispersion with band-edge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the non-Markovian dynamics we treat the quantum degrees of freedom of the nodes and connecting channel as a composite spin system with the surrounding of the quantum network as a Markovian bath, allowing for an efficient solution with time-dependent density matrix renormalization group techniques. We illustrate our approach showing non-Markovian effects in the driven-dissipative formation of quantum dimers, and we present examples for quantum information protocols involving quantum state transfer with engineered elements as basic building blocks of quantum spintronic circuits.
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2015

Articles

• B. Vermersch, A. Glätzle, P. Zoller Magic distances in the blockade mechanism of Rydberg p and d states, Phys. Rev. A 91 023411 (2015-02-11), http://dx.doi.org/10.1103/PhysRevA.91.023411 doi:10.1103/PhysRevA.91.023411 (ID: 719085) Toggle Abstract
  We show that the Rydberg blockade mechanism, which is well known in the case of s states, can be significantly different for p and d states due to the van der Waals couplings between different Rydberg Zeeman sublevels and the presence of a magnetic-field. We show, in particular, the existence of magic distances corresponding to the laser-excitation of a superposition of doubly excited states.
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• B. Vermersch, M. Punk, A. Glätzle, C. Gross, P. Zoller Dynamical preparation of laser-excited anisotropic Rydberg crystals in 2D optical lattices, New J. Phys. 17 013008 (2015-01-09), http://dx.doi.org/10.1088/1367-2630/17/1/013008 doi:10.1088/1367-2630/17/1/013008 (ID: 718969) Toggle Abstract
  We describe the dynamical preparation of anisotropic crystalline phases obtained by laser-exciting ultracold Alkali atoms to Rydberg p-states where they interact via anisotropic van derWaals interactions. We develop a timedependent variational mean field ansatz to model large, but finite two-dimensional systems in experimentally accessible parameter regimes, and we present numerical simulations to illustrate the dynamical formation of anisotropic Rydberg crystals.
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