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Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

Nature volume 534, pages 516519 (23 June 2016) | Download Citation


Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons1,2. 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 simulator3,4, 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 implemented5,6,7. 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 model8,9) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism10,11, 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 fields12 in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture13. 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.

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We acknowledge discussions with C. Hempel, E. R. Ortega and U. J. Wiese. Financial support was provided by the Austrian Science Fund (FWF), through the SFB FoQuS (FWF project nos F4002-N16 and F4016-N23), by the European Commission via the integrated project SIQS and the ERC synergy grant UQUAM, by the Deutsche Akademie der Naturforscher Leopoldina (grant nos LPDS 2013-07 and LPDR 2015-01), as well as the Institut für Quantenoptik und Quanteninformation GmbH. E.A.M. is a recipient of a DOC fellowship from the Austrian Academy of Sciences. P.S. was supported by the Austrian Science Foundation (FWF) Erwin Schrödinger Stipendium 3600-N27. This research was funded by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), through the Army Research Office grant W911NF-10-1-0284. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA, the ODNI, or the US Government.

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Author notes

    • Esteban A. Martinez
    •  & Christine A. Muschik

    These authors contributed equally to this work.


  1. Institute for Experimental Physics, University of Innsbruck, 6020 Innsbruck, Austria

    • Esteban A. Martinez
    • , Philipp Schindler
    • , Daniel Nigg
    • , Alexander Erhard
    • , Thomas Monz
    •  & Rainer Blatt
  2. Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria

    • Christine A. Muschik
    • , Markus Heyl
    • , Philipp Hauke
    • , Marcello Dalmonte
    • , Peter Zoller
    •  & Rainer Blatt
  3. Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria

    • Christine A. Muschik
    • , Philipp Hauke
    • , Marcello Dalmonte
    •  & Peter Zoller
  4. Physics Department, Technische Universität München, 85747 Garching, Germany

    • Markus Heyl


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E.A.M., C.A.M., M.D. and T.M. developed the research based on discussions with P.Z. and R.B.; E.A.M. and P.S. performed the experiments. E.A.M., C.A.M., P.S. and M.H. analysed the data and carried out numerical simulations. E.A.M., P.S., D.N., A.E. and T.M. contributed to the experimental setup. C.A.M., M.H., M.D., P.H. and P.Z. developed the theory. E.A.M., C.A.M., P.S., M.H., P.H., M.D., P.Z. and R.B. wrote the manuscript and provided revisions. All authors contributed to discussions of the results and the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Esteban A. Martinez or Christine A. Muschik.

Reviewer Information Nature thanks C. Wunderlich, E. Zohar and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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