A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical mechanics does not apply. The qubits are represented by trapped ion spins that can be prepared in a variety of initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with near 99% efficiency. This allows the single-shot measurement of arbitrary many-body correlations for the direct probing of the dynamical phase transition and the uncovering of computationally intractable features that rely on the long-range interactions and high connectivity between the qubits.There have been many recent demonstrations of quantum simulators with varying numbers of qubits and degrees of individual qubit control [1]. For instance, small numbers of qubits stored in trapped atomic ions [2,3] and superconducting circuits [4] have been used to simulate various magnetic spin or Hubbard models with individual qubit state preparation and measurement. Large numbers of atoms have simulated similar models, but with global control and measurements [5] or with correlations that only appear over a few atom sites [6]. An outstanding challenge is to increase qubit number while maintaining individual qubit control and measurement, with the goal of performing simulations or algorithms that cannot be efficiently solved classically. Atomic systems are excellent candidates for this scaling, because their qubits can be made virtually identical, with flexible and reconfigurable control through external optical fields and high initialization and detection efficiency for individual qubits. Recent work with neutral atoms [7,8] has demonstrated many-body quantum dynamics with up to 51 atoms coupled through van der Waals Rydberg interactions, and the current work presents the optical control and measurement of a similar number of atomic ions interacting through their long-range Coulomb-coupled motion.We perform a quantum simulation of a dynamical phase transition (DPT) with up to 53 trapped ion qubits. The understanding of such nonequilibrium behavior is of great interest to a wide range of subjects, from social science [9] and cellular biology [10] to astrophysics [11] and quantum condensed matter physics [12]. Recent theoretical studies of DPT [13][14][15][16][17][18][19][20] involve the transverse field Ising model (TFIM), the quintessential model of quantum phase transitions [21]. A recent experiment investigated a DPT with up to 10 trapped ion qubits, where the transverse field ...

The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated [1][2][3][4] and how difficult the system will be to describe numerically [5]. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective light cone [6]. However, little is known about the propagation speed in systems with long-range interactions, since the best long-range bound [7] is too loose to give the correct light-cone shape for any known spin model and since analytic solutions rarely exist. In this work, we experimentally determine the spatial and time-dependent correlations of a far-from-equilibrium quantum many-body system evolving under a long-range Ising-or XY-model Hamiltonian. For several different interaction ranges, we extract the shape of the light cone and measure the velocity with which correlations propagate through the system. In many cases we find increasing propagation velocities, which violate the Lieb-Robinson prediction, and in one instance cannot be explained by any existing theory. Our results demonstrate that even modestly-sized quantum simulators are well-poised for studying complicated many-body systems that are intractable to classical computation.Lieb-Robinson bounds [6] have strongly influenced our understanding of locally-interacting quantum many-body systems. These bounds restrict the many-body dynamics to a well-defined causal region outside of which correlations are exponentially suppressed [8], analogous to causal light cones that arise in relativistic theories. Their existence has enabled proofs linking the decay of correlations in ground states to the presence of a spectral gap [7,9], as well as the area law for entanglement entropy [5,10,11], which can indicate the computational complexity of classically simulating a quantum system. Furthermore, Lieb-Robinson bounds constrain the timescales on which quantum systems might thermalize [12][13][14] and the maximum speed with which information can be sent through a quantum channel [15]. Recent experimental work has observed an effective Lieb-Robinson (i.e. linear) light cone in a 1D quantum gas [16].When interactions in a quantum system are longrange, the speed with which correlations build up between distant particles is no longer guaranteed to obey the Lieb-Robinson prediction. Indeed, for sufficiently long-ranged interactions, the notion of locality is expected to break down completely [17]. Violation of the Lieb-Robinson bound means that comparatively little can be predicted about the growth and propagation of correlations in long-range interacting systems, though there have been several recent theoretical and numerical advances [2,3,7,[17][18][19].Here we report an experiment that directly measures the shape of the causal region and the speed at which correlations propagate within Ising and XY spin chains. To induce the spread of correlations, we perform a global q...