Fidelity Witnesses for Fermionic Quantum Simulations

M. Gluza, M. Kliesch, J. Eisert, and L. Aolita
Phys. Rev. Lett. 120, 190501 – Published 11 May 2018
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Abstract

The experimental interest and developments in quantum spin-1/2 chains has increased uninterruptedly over the past decade. In many instances, the target quantum simulation belongs to the broader class of noninteracting fermionic models, constituting an important benchmark. In spite of this class being analytically efficiently tractable, no direct certification tool has yet been reported for it. In fact, in experiments, certification has almost exclusively relied on notions of quantum state tomography scaling very unfavorably with the system size. Here, we develop experimentally friendly fidelity witnesses for all pure fermionic Gaussian target states. Their expectation value yields a tight lower bound to the fidelity and can be measured efficiently. We derive witnesses in full generality in the Majorana-fermion representation and apply them to experimentally relevant spin-1/2 chains. Among others, we show how to efficiently certify strongly out-of-equilibrium dynamics in critical Ising chains. At the heart of the measurement scheme is a variant of importance sampling specially tailored to overlaps between covariance matrices. The method is shown to be robust against finite experimental-state infidelities.

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  • Received 26 May 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.190501

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

M. Gluza1, M. Kliesch2,3, J. Eisert1, and L. Aolita4,5,6

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Germany
  • 2Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Poland
  • 3Institute for Theoretical Physics, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
  • 4Instituto de Física, Universidade Federal do Rio de Janeiro, P.O. Box 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
  • 5International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil
  • 6ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, UNESP-Universidade Estadual Paulista R. Dr. Bento T. Ferraz 271, Bl. II, São Paulo 01140-070, São Paulo, Brazil

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Issue

Vol. 120, Iss. 19 — 11 May 2018

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