• Open Access

Exploring Interacting Quantum Many-Body Systems by Experimentally Creating Continuous Matrix Product States in Superconducting Circuits

C. Eichler, J. Mlynek, J. Butscher, P. Kurpiers, K. Hammerer, T. J. Osborne, and A. Wallraff
Phys. Rev. X 5, 041044 – Published 16 December 2015

Abstract

Improving the understanding of strongly correlated quantum many-body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research, and chemistry. Enormous progress has been made in the past decades in developing both classical and quantum approaches to calculate, simulate, and experimentally probe the properties of such systems. In this work, we use a combination of classical and quantum methods to experimentally explore the properties of an interacting quantum gas by creating experimental realizations of continuous matrix product states—a class of states that has proven extremely powerful as a variational ansatz for numerical simulations. By systematically preparing and probing these states using a circuit quantum electrodynamics system, we experimentally determine a good approximation to the ground-state wave function of the Lieb-Liniger Hamiltonian, which describes an interacting Bose gas in one dimension. Since the simulated Hamiltonian is encoded in the measurement observable rather than the controlled quantum system, this approach has the potential to apply to a variety of models including those involving multicomponent interacting fields. Our findings also hint at the possibility of experimentally exploring general properties of matrix product states and entanglement theory. The scheme presented here is applicable to a broad range of systems exploiting strong and tunable light-matter interactions.

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  • Received 20 August 2015

DOI:https://doi.org/10.1103/PhysRevX.5.041044

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

C. Eichler1,*, J. Mlynek1, J. Butscher1, P. Kurpiers1, K. Hammerer2,3,4, T. J. Osborne2, and A. Wallraff1

  • 1Department of Physics, ETH Zürich, CH-8093 Zürich, Switzerland
  • 2Institute for Theoretical Physics, Leibniz University, 30167 Hannover, Germany
  • 3Institut für Gravitationsphysik, Leibniz Universität, 30167 Hannover, Germany
  • 4Max-Planck Institut für Gravitationsphysik (Albert-Einstein Institut), 30167 Hannover, Germany

  • *Present address: Department of Physics, Princeton University, Princeton, NJ 08544, USA. ceichler@princeton.edu

Popular Summary

Entanglement correlations between particles constitute one of the most striking phenomena in quantum physics. Many key properties of materials, such as superconductivity or magnetism, are governed by those intricate quantum relations between particles. Understanding and modeling these complex properties are often based on a systematic restriction of the underlying parameter space to its relevant part. Here, we explore this concept using a quantum computing device rather than a classical computer.

By employing a fully controlled cavity quantum electrodynamic system made of superconducting circuits, we experimentally create matrix product states, a class of states that has proven to be extremely powerful as a variational ansatz for numerical simulations. We create 1000 such quantum states and efficiently probe their correlation properties to determine an approximation to the ground state of a model describing a gas of interacting quantum particles. Having physical access to the simulated ground-state wave functions enables us to also probe higher-order correlation functions beyond measuring the ground-state energy. The experimental data are in good agreement with the exact solution over a wide range of interaction strengths of the model.

Our experiments shed light on surprising connections between the physics of ultracold gases, cavity quantum electrodynamics, and novel concepts of quantum information theory. We expect that our findings will lay the groundwork for yet-unexplored approaches to quantum simulation applicable to problems in material science, physics, chemistry, and biology.

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Vol. 5, Iss. 4 — October - December 2015

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It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

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