The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around many-body 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 [1]. Here we report on the observation of magnon quasiparticle dynamics in a one-dimensional many-body quantum system of trapped ions representing an Ising spin model [2,3]. Using the ability to tune the effective interaction range [4][5][6], 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 many-body system. Second, for long-range interactions we observe the divergence of quasiparticle velocity and breakdown of the light-cone picture [7][8][9][10] that is valid for short-range interactions. Our results will allow experimental studies of a wide range of phenomena, such as quantum transport [11,12], thermalisation [13], localisation [14] and entanglement growth [15], and represent a first step towards a new quantum-optical regime with on-demand quasiparticles with tunable non-linear interactions.Quasiparticles, such as magnons, phonons, and anyons, are elementary excitations in the collective behaviour of an underlying many-body quantum system. While precise control is already possible in the laboratory for systems of individual atoms, ions, or photons, it remains a challenge to extend this to quasiparticles. In systems with nearest-neighbour interactions, quasiparticles are expected to distribute entanglement within light-like-cones defined by a strict quantum information speed limit, enforced not by relativity but by the finite interaction range itself [7,16,17]. These results, known as Lieb-Robinson bounds, have allowed various important theorems to be proven about systems with nearest-neighbour interactions, including restrictions on ground-state correlations [18,19] and the time to create states for topological quantum computation [16]. Recently, wavefronts of correlations have been observed in bosonic atoms in optical lattices with nearest-neighbour interactions [20,21], and an outstanding challenge is to observe the entanglement dynamics.Extending these results to systems with long-range interactions is of great interest: the interactions in many natural systems fall into this class, exhibiting a power-law dependence (1/r α ), such as van-der-Waals (α=6), dipole-dipole (α=3), or Coulomb interactions (α=1). In each case, a new set of quasiparticles are predicted with unique properties. If the interactions fall off sufficiently fast, one can still formulate generalized Lieb-Robinson bounds [8][9][10]. However, the notion of a speed of information propagation becomes invalid. For even longer-range interactions, these bounds...

Quantum-classical hybrid algorithms are emerging as promising candidates for near-term 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 cross-platform benchmark for multi-qubit quantum simulators.

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.Engineered quantum systems, consisting of tens of individually-controllable interacting quantum particles, are currently being developed using a number of different physical platforms; including atoms in optical arrays (1-3), ions in radio-frequency traps (4, 5), and superconducting circuits (6-9). These systems offer the possibility of generating and 1 arXiv:1806.05747v2 [quant-ph] 14 Jan 2019 probing complex quantum states and dynamics particle by particle -finding application in the near-term as quantum simulators, and in the longer-term as quantum computers. As these systems are developed, new protocols are required to characterize them -to verify that they are performing as desired and to measure quantum phenomena of interest.A key property to measure in engineered quantum systems is entanglement. For example, in order for quantum simulators and computers to provide an advantage over their classical analogues, they must generate large amounts of entanglement between their parts (10). Furthermore, when using these devices to tackle open questions in physics, the dynamics of entanglement provides signatures of the phenomena of interest, such as thermalization (11) and many-body localization (12,13).Entanglement can be probed by measuring entanglement entropies. In particular, consider the second-order Rényi entropywith ρ A the reduced density matrix for a part A of the total system described by ρ. If the entropy of part A is greater than the entropy of the total system; i.e S (2) (ρ A ) > S (2) (ρ), bipartite entanglement exists between A and the rest of the system (14). Thus, a measurement of the entropy of the whole system, as well as of its subsystems, provides information about the entanglement contained within the system. Additionally, a measurement of the entropy of the total state ρ provides the opportunity to verify the overall coherence of the system, as for pure quantum states S (2) (ρ) = 0.Recently, a protocol to directly measure the second-order Rényi entropy, S (2) , has been demonstrated, requiring collective measurements to be made on two identical copies ρ of a quantum system (15)(16)(17)(18). In (17), that protocol was used to study entanglement growth and thermali...

Dynamical quantum phase transitions (DQPTs) extend the concept of phase transitions and thus universality to the non-equilibrium regime. In this letter, we investigate DQPTs in a string of ions simulating interacting transverse-field Ising models. We observe non-equilibrium 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 non-analytic 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.Today, the equilibrium properties of quantum matter are theoretically described with remarkable success. Yet, in recent years pioneering experiments have created novel quantum states beyond this equilibrium paradigm [1,2]. Thanks to this progress, it is now possible to experimentally study exotic phenomena such as many-body localization [3,4], prethermalization [5, 6], particle-antiparticle production in the lattice Schwinger model [7], and light-induced superconductivity [8]. Understanding general properties of such nonequilibrium quantum states provides a significant challenge, calling for new concepts that extend important principles such as universality to the non-equilibrium realm. A general approach towards this major goal is the theory of dynamical quantum phase transitions (DQPTs) [9], which extends the concept of phase transitions and thus universality to the nonequilibrium regime. In this letter, we directly observe the defining real-time non-analyticities at DQPTs in a trappedion quantum simulator for interacting transverse-field Ising models. 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. Our work advances towards experimentally characterizing nonequilibrium quantum states and their dynamics, by offering general experimental tools that can be applied also to other inherently dynamical phenomena.Statistical mechanics and thermodynamics provide us with an excellent understanding of equilibrium quantum manybody systems. A key concept in this framework is the canonical partition function Z(T ) = Tr(e −H/k B T ), with T the temperature, k B the Boltzmann constant, and H the system Hamiltonian. The partition function encodes thermodynamics via the free-energy density f = −(k B T/N) log [Z(T )], where N de- * Present address:ARC Centre of Excellence for Engineered Quantum Systems, School of Physics, University of Sydney, NSW, 2006, Australia notes the number of degrees of freedom. A phase transition, i.e., a sudden change of macroscopic behaviour, is associated with a non-analytical behaviour of f as a function of temperature or another control parameter g such as an external magnetic field. Quantum phase transitions (QPTs) [10] occur when T is kept at absolute zero, where the system's groundstate properties undergo a non-analyt...

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We generate and characterise 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 out-of-equilibrium dynamics of an Ising-type Hamiltonian, engineered via laser fields. Since the qubit-qubit interactions decay with distance, entanglement is generated at early times predominantly between neighbouring groups of qubits. We characterise entanglement between these groups by designing and applying witnesses for genuine multipartite entanglement. Our results show that, during the dynamical evolution, all neighbouring 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.

We improve the quality of quantum circuits on superconducting quantum computing systems, as measured by the quantum volume (QV), with a combination of dynamical decoupling, compiler optimizations, shorter two-qubit gates, and excited state promoted readout. This result shows that the path to larger QV systems requires the simultaneous increase of coherence, control gate fidelities, measurement fidelities, and smarter software which takes into account hardware details, thereby demonstrating the need to continue to co-design the software and hardware stack for the foreseeable future.

Quantum state tomography is the standard technique for estimating the quantum state of small systems 1 . But its application to larger systems soon becomes impractical as the required resources scale exponentially with the size. Therefore, considerable e ort is dedicated to the development of new characterization tools for quantum many-body states 2-11 . Here we demonstrate matrix product state tomography 2 , which is theoretically proven to allow for the e cient and accurate estimation of a broad class of quantum states. We use this technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled and individually controlled spins: a size far beyond the practical limits of quantum state tomography. Our results reveal the dynamical growth of entanglement and describe its complexity as correlations spread out during a quench: a necessary condition for future demonstrations of better-than-classical performance. Matrix product state tomography should therefore find widespread use in the study of large quantum many-body systems and the benchmarking and verification of quantum simulators and computers.A matrix product state (MPS) is a way of expressing a manyparticle wavefunction which, for a broad class of physical states, offers a compact and accurate description with a number of parameters that increases only polynomially (that is, efficiently) in system components 12 . MPS tomography recognizes that the information required to identify the compact MPS is typically accessible locally; that is, by making measurements only on subsets of particles that lie in the same neighbourhood 2 . In such cases, the total effort required to obtain a reliable estimate for the state in the laboratory increases at most polynomially in system components 2,6 . States suited to MPS tomography and its generalizations to higher dimensions 2 include those with a maximum distance over which significant quantum correlations exist between constituents (locally correlated states): for example, the 2D cluster states-universal resource states for quantum computing-and the ground states of a broad class of one-dimensional (1D) systems [13][14][15] . We find that MPS tomography is also well-suited to characterize the states generated during the dynamical evolution of systems with shortranged interactions, as found in many physical systems.Consider an N -component quantum system initially in a product state (or other locally correlated state) in which interactions are abruptly turned on. In the presence of finite-range interactions, information and correlations spread out in the system with a strict maximum group velocity [16][17][18] . Therefore, after a finite evolution time, there is a maximum distance over which correlations extend in the system (the correlation length, L), beyond which correlations decay exponentially in distance. The information required to describe the state is largely contained in the local reductions: the reduced states (density matrices) of all groups of neighbouring particles...