Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons [1,2]. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator [3,4], this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented [5][6][7]. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model [8,9]) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism [10,11], describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields [12] in favour of exotic longrange interactions, which have a direct and efficient implementation on an ion trap architecture [13]. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments, the long-term vision being the extension to real-time quantum simulations of non-Abelian lattice gauge theories.Small-scale quantum computers exist today in the laboratory as programmable quantum devices [14]. In particular, trapped-ion quantum computers [13] provide a platform allowing a few hundred coherent quantum gates on a few qubits, with a clear roadmap towards scaling up FIG. 1. (a)The instability of the vacuum due to quantum fluctuations is one of the most fundamental effects in gauge theories. We simulate the coherent real time dynamics of particle-antiparticle creation by realising the Schwinger model (one-dimensional quantum electrodynamics) on a lattice, as described in the main text. (b) The experimental setup for the simulation consists of a linear Paul trap, where a string of 40 Ca + ions is confined. The electronic states of each ion encode a spin |↑ or |↓ ; these can be manipulated using laser beams (see Methods for details).these devices [4,15]. This provides the tools for universal digital quantum simulation [16], where the time evolution of a quantum system is approximated as a stroboscopic sequence of quantum gates [17]. Here we show how this quantum technology can be used to simulate the real time dynamics of a minimal model of a lattice gauge theory, realising the Schwinge...

Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment, where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser-and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04s at room temperature. Our system consists of two ensembles containing about 10 12 atoms and separated by 0.5m coupled to the environment composed of the vacuum modes of the electromagnetic field. By combining the dissipative mechanism with a continuous measurement, steady state entanglement is continuously generated and observed for up to an hour. PACS numbers:To date, experiments investigating quantum superpositions and entanglement are hampered by decoherence. Its effects have been studied in several systems [1]. However, it was recognized [2] that the engineered interaction with a reservoir can drive the system into a desired steady state. In particular, dissipation common for two systems can drive them into an entangled state [3]. The idea of using and engineering dissipation rather than relying on coherent evolutions only, represents a paradigm shift with potentially significant practical advantages. Contrary to other methods, entanglement generation by dissipation does not require the preparation of a system in a particular input state and exists, in principle, for an arbitrary long time, which is expected to play an important role in quantum information protocols [4][5][6][7]. These features make dissipative methods inherently stable against weak random perturbations, with the dissipative dynamics stabilizing the entanglement.We report on the first demonstration of purely dissipative entanglement generation [8]. In contrast to previous approaches [9][10][11], entanglement is obtained without using measurements on the quantum state of the environment (i.e. the light field). The dissipation-based method implemented here is deterministic and unconditional and therefore fundamentally different from standard approaches such as the QND-based method [9] or the DLCZ protocol [4], which yield a separable state if the emitted photons are not detected. Furthermore, we report the creation of a steady state atomic entanglement by combining the dissipative mechanism proposed in [12] with continuous measurements. The generated entanglement is of the EPR type, which plays a central role in continuous variable quantum information processing [6,13], quantum sensing [14] and metrology [11,15,16]. Fig. 1a presents the principles of engineered dissipation in our system consisting of two 133 Cs ensembles, interacting with a y-polarized laser field at ω L . A pair of twolevel systems is encoded in the 6S 1/2 ground state sublevels |↑ I ≡ |4, 4 I , |↓ I ≡ |4, 3 I and |↑ II ≡ |4, −3 II , |↓ II ≡ |4, −4 II . Operators J ± I/II with J ...

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