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 ...

We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/r α ) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic bound states in high-energy physics. We show that these quasiparticles have signatures in the dynamics of order parameters following a global quench and the Fourier spectrum of these order parameters can be expolited as a direct probe of the masses of the confined quasiparticles. We introduce a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement, and to quantitatively predict the masses of the bound quasiparticles. Furthermore, we illustrate that these quasiparticle states can lead to slow thermalization of onepoint observables for certain initial states. Our work is readily applicable to current trapped-ion experiments.Long-range interacting quantum systems occur naturally in numerous quantum simulators [1][2][3][4][5][6][7][8][9][10]. A paradigmatic model considers interactions decaying with distance r as a power law 1/r α . This describes the interaction term in trappedion spin systems [3,[11][12][13][14][15], polar molecules [16][17][18][19], magnetic atoms [5,20,21], and Rydberg atoms [1,2,22,23]. One remarkable consequence of long-range interactions is the breakdown of locality, where quantum information, bounded by linear 'light cones' in short-range interacting systems [24], can propagate super-ballistically or even instantaneously [25][26][27][28][29][30]. Lieb-Robinson linear light cones have been generalized to logarithmic and polynomial light cones for long-range interacting systems [25,26,31], and non-local propagation of quantum correlations in one-dimensional (1D) spin chains has been observed in trapped-ion experiments [12,13]. Moreover, 1D long-range interacting quantum spin chains can host novel physics that is absent in their short-range counterparts, such as continuous symmetry breaking [32,33].More recently, it has been shown that confinement-which has origins in high-energy physics-has dramatic signatures in the quantum quench dynamics of short-range interacting spin chains [34]. Owing to confinement, quarks cannot be directly observed in nature as they form mesons and baryons due to strong interactions [35,36]. An archetypal model with analogous confinement effects in quantum many-body systems is the 1D short-range interacting Ising model with both transverse and longitudinal fields [37][38][39][40][41][42]. For a vanishing longitudinal field, domain-wall quasiparticles propagate freely and map out light-cone spreading of quantum information [41][42][43][44]. As first proposed by , a nonzero longitudinal field induces an attractive linear potential between two domain walls and confines them into mesonic bound quasiparticles. Recently, Kormos et al. investigated the effect of these bound states on quench dynamics and showed that the non...