title: Real-time dynamics of lattice gauge theories with a few-qubit quantum computer.
abstract: Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman's idea of a quantum simulator, 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. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, 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 in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. 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 simulation of high-energy theories using atomic physics experiments-the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.
authors.affiliation: Institute for Experimental Physics, University of Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Esteban A
authors.initials: EA
authors.lastname: Martinez
authors.affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria.|Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Christine A
authors.initials: CA
authors.lastname: Muschik
authors.affiliation: Institute for Experimental Physics, University of Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Philipp
authors.initials: P
authors.lastname: Schindler
authors.affiliation: Institute for Experimental Physics, University of Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Daniel
authors.initials: D
authors.lastname: Nigg
authors.affiliation: Institute for Experimental Physics, University of Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Alexander
authors.initials: A
authors.lastname: Erhard
authors.affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria.|Physics Department, Technische Universität München, 85747 Garching, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Heyl
authors.affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria.|Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Philipp
authors.initials: P
authors.lastname: Hauke
authors.affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria.|Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Marcello
authors.initials: M
authors.lastname: Dalmonte
authors.affiliation: Institute for Experimental Physics, University of Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Thomas
authors.initials: T
authors.lastname: Monz
authors.affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria.|Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria.
authors.forename: Peter
authors.initials: P
authors.lastname: Zoller
authors.affiliation: Institute for Experimental Physics, University of Innsbruck, 6020 Innsbruck, Austria.|Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria.
authors.forename: Rainer
authors.initials: R
authors.lastname: Blatt