
C. Hempel, C. Maier, J. Romero, J. McClean, T. Monz, H. Shen, P. Jurcevic, B. P. Lanyon, P. Love, R. Babbush, A. AspuruGuzik, R. Blatt, C. F. Roos Quantum chemistry calculations on a trappedion quantum simulator,
Phys. Rev. X 8 31022 (20180724),
http://dx.doi.org/10.1103/PhysRevX.8.031022 doi:10.1103/PhysRevX.8.031022 (ID: 720003)
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Quantumclassical hybrid algorithms are emerging as promising candidates for nearterm practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a crossplatform benchmark for multiqubit quantum simulators.

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 (20180618),
http://dx.doi.org/10.1126/science.aau4963 doi:10.1126/science.aau4963 (ID: 720034)
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Entanglement is the key feature of manybody 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 trappedion 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.

N. Friis, O. Marty, C. Maier, C. Hempel, M. Holzapfel, P. Jurcevic, M. Plenio, M. Huber, C. F. Roos, R. Blatt, B. P. Lanyon Observation of Entangled States of a Fully Controlled 20Qubit System,
Phys. Rev. X 8 21012 (20180410),
http://dx.doi.org/10.1103/PhysRevX.8.021012 doi:10.1103/PhysRevX.8.021012 (ID: 720009)
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We generate and characterize entangled states of a register of 20 individually controlled qubits, where each qubit is encoded into the electronic state of a trapped atomic ion. Entanglement is generated amongst the qubits during the outofequilibrium dynamics of an Isingtype Hamiltonian, engineered via laser fields. Since the qubitqubit interactions decay with distance, entanglement is generated at early times predominantly between neighboring groups of qubits. We characterize entanglement between these groups by designing and applying witnesses for genuine multipartite entanglement. Our results show that, during the dynamical evolution, all neighboring qubit pairs, triplets, most quadruplets, and some quintuplets simultaneously develop genuine multipartite entanglement. Witnessing genuine multipartite entanglement in larger groups of qubits in our system remains an open challenge.

B. P. Lanyon, C. Maier, M. Holzapfel, T. Baumgratz, C. Hempel, P. Jurcevic, I. Dhand, A. S. Buyskik, A. J. Daley, M. Cramer, M. Plenio, R. Blatt, C. F. Roos Efficient tomography of a quantum manybody system,
Nature Phys. 13 1158 (20171205),
http://dx.doi.org/10.1038/nphys4244 doi:10.1038/nphys4244 (ID: 719716)
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Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes impractical as the effort required grows exponentially in the number of constituents. Developing more efficient techniques is particularly pressing as preciselycontrollable quantum systems that are well beyond the reach of QST are emerging in laboratories. Motivated by this, there is a considerable ongoing effort to develop new characterisation tools for quantum manybody systems. Here we demonstrate Matrix Product State (MPS) tomography, which is theoretically proven to allow the states of a broad class of quantum systems to be accurately estimated with an effort that increases efficiently with constituent number. We first prove that this broad class includes the outofequilbrium states produced by 1D systems with finiterange interactions, up to any fixed point in time. We then use the technique to reconstruct the dynamical state of a trappedion quantum simulator comprising up to 14 entangled spins (qubits): a size far beyond the reach of QST. Our results reveal the dynamical growth of entanglement and description complexity as correlations spread out during a quench: a necessary condition for future beyondclassical performance. MPS tomography should find widespread use to study large quantum manybody systems and to benchmark and verify quantum simulators and computers.

V. Krutyanskiy, M. R. Meraner, J. Schupp, B. P. Lanyon Polarisationpreserving photon frequency conversion from a trappedioncompatible wavelength to the telecom Cband,
Appl. Phys. B Las. Opt. 123 228 (20170930),
http://dx.doi.org/10.1007/s0034001768068 doi:10.1007/s0034001768068 (ID: 719939)
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We demonstrate polarisationpreserving frequency conversion of singlephotonlevel light at 854 nm, resonant with a trappedion transition and qubit, to the 1550nm telecom C band. A total photon in / fibercoupled photon out efficiency of ∼30% is achieved, for a freerunning photon noise rate of ∼60 Hz. This performance would enable telecom conversion of 854 nm polarisation qubits, produced in existing trappedion systems, with a signaltonoise ratio greater than 1. In combination with nearfuture trappedion systems, our converter would enable the observation of entanglement between an ion and a photon that has travelled more than 100 km in optical fiber: three orders of magnitude further than the stateoftheart.

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 (20170908),
http://dx.doi.org/10.1088/20589565/aa868b doi:10.1088/20589565/aa868b (ID: 719794)
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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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P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, C. F. Roos Direct observation of dynamical quantum phase transitions in an interacting manybody system,
Phys. Rev. Lett. 119 80501 (20170821),
http://dx.doi.org/10.1103/PhysRevLett.119.080501 doi:10.1103/PhysRevLett.119.080501 (ID: 719714)
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Dynamical quantum phase transitions (DQPTs) extend the concept of phase transitions and thus universality
to the nonequilibrium regime. In this letter, we investigate DQPTs in a string of ions simulating interacting transversefield Ising models. We observe nonequilibrium dynamics induced by a quantum quench and show for strings of up to 10 ions the direct detection of DQPTs by measuring a quantity that becomes nonanalytic in time in the thermodynamic limit. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.
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M. Zwerger, B. P. Lanyon, T. E. Northup, C. A. Muschik, W. Dür, N. Sangouard Quantum repeaters based on trapped ions with decoherencefree subspace encoding,
Quantum Sci. Technol. 2 44001 (20170804),
http://dx.doi.org/10.1088/20589565/aa7983 doi:10.1088/20589565/aa7983 (ID: 719938)
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Quantum repeaters provide an efficient solution to distribute Bell pairs over arbitrarily long distances. While scalable architectures are demanding regarding the number of qubits that need to be controlled, here we present a quantum repeater scheme aiming to extend the range of present day quantum communications that could be implemented in the near future with trapped ions in cavities. We focus on an architecture where ionphoton entangled states are created locally and subsequently processed with linear optics to create elementary links of ionion entangled states. These links are then used to distribute entangled pairs over long distances using successive entanglement swapping operations performed using deterministic ionion gates. We show how this architecture can be implemented while encoding the qubits in a decoherencefree subspace to protect them against collective dephasing. This results in a protocol that can be used to violate a Bell inequality over distances of about 800 km assuming stateoftheart parameters. We discuss how this could be improved to several thousand kilometres in future setups.

P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, C. F. Roos Quasiparticle engineering and entanglement propagation in a quantum manybody system,
Nature 511 202 (20140710),
http://dx.doi.org/10.1038/nature13461 doi:10.1038/nature13461 (ID: 718717)
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The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around manybody systems. Furthermore, the controlled distribution of entanglement is of fundamental importance for quantum communication and computation. In many situations, quasiparticles are the carriers of information around a quantum system and are expected to distribute entanglement in a fashion determined by the system interactions. Here we report on the observation of magnon quasiparticle dynamics in a onedimensional manybody quantum system of trapped ions representing an Ising spin model. Using the ability to tune the effective interaction range, and to prepare and measure the quantum state at the individual particle level, we observe new quasiparticle phenomena. For the first time, we reveal the entanglement distributed by quasiparticles around a manybody system. Second, for longrange interactions we observe the divergence of quasiparticle velocity and breakdown of the lightcone picture that is valid for shortrange interactions. Our results will allow experimental studies of a wide range of phenomena, such as quantum transport, thermalisation, localisation and entanglement growth, and represent a first step towards a new quantumoptical regime with ondemand quasiparticles with tunable nonlinear interactions.
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B. P. Lanyon, M. Zwerger, P. Jurcevic, C. Hempel, W. Dür, H. J. Briegel, R. Blatt, C. F. Roos Experimental Violation of Multipartite Bell Inequalities with Trapped Ions,
Phys. Rev. Lett. 112 100403 (20140313),
http://dx.doi.org/10.1103/PhysRevLett.112.100403 doi:10.1103/PhysRevLett.112.100403 (ID: 718697)
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We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First, we consider resource states for measurementbased quantum computation of between 3 and 7 ions and show that all strongly violate a Belltype inequality for graph states, where the criterion for violation is a sufficiently high fidelity. Second, we analyze GreenbergerHorneZeilinger states of up to 14 ions generated in a previous experiment using stronger MerminKlyshko inequalities, and show that in this case the violation of local realism increases exponentially with system size. These experiments represent a violation of multipartite Belltype inequalities of deterministically prepared entangled states. In addition, the detection loophole is closed.

S. Genway, W. Li, C. Ates, B. P. Lanyon, I. Lesanovsky Generalized Dicke Nonequilibrium Dynamics in Trapped Ions,
Phys. Rev. Lett. 112 023603 (20140117),
http://dx.doi.org/10.1103/PhysRevLett.112.023603 doi:10.1103/PhysRevLett.112.023603 (ID: 718711)
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We explore trapped ions as a setting to investigate nonequilibrium phases in a generalized Dicke model of dissipative spins coupled to phonon modes. We find a rich dynamical phase diagram including superradiantlike regimes, dynamical phase coexistence, and phononlasing behavior. A particular advantage of trapped ions is that these phases and transitions among them can be probed in situ through fluorescence. We demonstrate that the main physical insights are captured by a minimal model and consider an experimental realization with Ca+ ions trapped in a linear Paul trap with a dressing scheme to create effective twolevel systems with a tunable dissipation rate.

B. P. Lanyon, P. Jurcevic, M. Zwerger, C. Hempel, E. A. Martínez, W. Dür, H. J. Briegel, R. Blatt, C. F. Roos Measurementbased quantum computation with trapped ions,
Phys. Rev. Lett. 111 210501 (20131119),
http://dx.doi.org/10.1103/PhysRevLett.111.210501 doi:10.1103/PhysRevLett.111.210501 (ID: 718582)
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Measurementbased quantum computation represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the oneway quantum computer, with the cluster state as its universal resource. Here we demonstrate the principles of measurementbased quantum computation using deterministically generated cluster states, in a system of trapped calcium ions. First we implement a universal set of operations for quantum computing. Second we demonstrate a family of measurementbased quantum error correction codes and show their improved performance as the code length is increased. The methods presented can be directly scaled up to generate graph states of several tens of qubits.

B. P. Lanyon, P. Jurcevic, C. Hempel, M. Gessner, V. Vedral, R. Blatt, C. F. Roos Experimental generation of quantum discord via noisy processes,
Phys. Rev. Lett. 111 100504 (20130906),
http://dx.doi.org/10.1103/PhysRevLett.111.100504 doi:10.1103/PhysRevLett.111.100504 (ID: 718585)
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Quantum systems in mixed states can be unentangled and yet still nonclassically correlated. These correlations can be quantified by the quantum discord and might provide a resource for quantum information processing tasks. By precisely controlling the interaction of two ionicqubits with their environment, we investigate the capability of noise to generate discord. Firstly we show that noise acting only one quantum system can generate discord between two. States generated in this way are restricted in terms of the rank of their correlation matrix. Secondly we show that classicallycorrelated noise processes are capable of generating a much broader range of discordant states, with correlation matrices of any rank. Our results show that noise processes, prevalent in many physical systems, can automatically generate nonclassical correlations and highlight fundamental differences between discord and entanglement.

C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, C. F. Roos Entanglementenhanced detection of singlephoton scattering events,
Nature Photon. 7 633 (20130730),
http://dx.doi.org/10.1038/nphoton.2013.172 doi:10.1038/nphoton.2013.172 (ID: 718575)
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The ability to detect the interaction of light and matter at the singleparticle level is becoming increasingly important for many areas of science and technology. The absorption or emission of a photon on a narrow transition of a trapped ion can be detected with near unit probability, thereby enabling the realization of ultraprecise ion clocks and quantum information processing applications. Extending this sensitivity to broad transitions is challenging due to the difficulty of detecting the rapid photon scattering events in this case. Here, we demonstrate a technique to detect the scattering of a single photon on a broad optical transition with high sensitivity. Our approach is to use an entangled state to amplify the tiny momentum kick an ion receives upon scattering a photon. The method should find applications in spectroscopy of atomic and molecular ions and quantum information processing.

J. Schachenmayer, B. P. Lanyon, C. F. Roos, A. J. Daley Entanglement growth in quench dynamics with variable range interactions,
Phys. Rev. X 3 031015 (20130530),
http://dx.doi.org/10.1103/PhysRevX.3.031015 doi:10.1103/PhysRevX.3.031015 (ID: 718525)
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Studying entanglement growth in quantum dynamics provides both insight into the underlying microscopic processes, and information about the complexity of the quantum states, which is related to the efficiency of simulations on classical computers. Recently, experiments with trapped ions, polar molecules, and Rydberg excitations have provided new opportunities to observe dynamics with long range interactions. We explore nonequilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spinspin interactions in a transverse Ising chain is varied. Computing the buildup of bipartite entanglement as well as mutual information between distant spins, we identify linear growth of entanglement entropy corresponding to propagation of quasiparticles for shorter range interactions, with the maximum rate of growth occurring when the Hamiltonian parameters match those for the quantum phase transition. Counterintuitively, the growth of bipartite entanglement for longrange interactions is only logarithmic for most regimes, i.e., substantially slower than for shorter range interactions. Experiments with trapped ions allow for the realization of this system with tunable interaction range, and we show that the different phenomena are robust for finite systems sizes and in the presence of noise. These results can act as a direct guide for the generation of largescale entanglement in such experiments, towards a regime where the entanglement growth can render existing classical simulations inefficient.

L. Lamata, C. E. Lopez, B. P. Lanyon, T. Bastin, J. C. Retamal, E. Solano Deterministic generation of arbitrary symmetric states and entanglement classes,
Phys. Rev. A 87 032325 (20130327),
http://dx.doi.org/10.1103/PhysRevA.87.032325 doi:10.1103/PhysRevA.87.032325 (ID: 718473)
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We propose a method to generate arbitrary symmetric states of N qubits, which can be easily associated with their entanglement classes. It is particularly suited to quantum optics systems like trapped ions or superconducting circuits.We encode each qubit in two metastable levels of the system and use a bosonic quantum bus for creating the states. The method is deterministic and relies on a sequence of selective unitary gates upon the qubits within the system coherence time.