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Quantum error-detection at low energies

  • Regular Article - Theoretical Physics
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  • Published: 03 September 2019
  • volume 2019, Article number: 21 (2019)
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Quantum error-detection at low energies
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  • Martina Gschwendtner1,
  • Robert König1,2,
  • Burak Şahinoğlu3 &
  • …
  • Eugene Tang3 

  • 388 Accesses

  • 4 Citations

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  • Cite this article

A preprint version of the article is available at arXiv.

Abstract

Motivated by the close relationship between quantum error-correction, topological order, the holographic AdS/CFT duality, and tensor networks, we initiate the study of approximate quantum error-detecting codes in matrix product states (MPS). We first show that using open-boundary MPS to define boundary to bulk encoding maps yields at most constant distance error-detecting codes. These are degenerate ground spaces of gapped local Hamiltonians. To get around this no-go result, we consider excited states, i.e., we use the excitation ansatz to construct encoding maps: these yield error-detecting codes with distance Ω(n1−ν ) for any ν ∈ (0, 1) and Ω(log n) encoded qubits. This shows that gapped systems contain — within isolated energy bands — error-detecting codes spanned by momentum eigenstates. We also consider the gapless Heisenberg-XXX model, whose energy eigenstates can be described via Bethe ansatz tensor networks. We show that it contains — within its low-energy eigenspace — an error-detecting code with the same parameter scaling. All these codes detect arbitrary d-local (not necessarily geometrically local) errors even though they are not permutation-invariant. This suggests that a wide range of naturally occurring many-body systems possess intrinsic error-detecting features.

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Authors and Affiliations

  1. Zentrum Mathematik, Technical University of Munich, 85748, Garching, Germany

    Martina Gschwendtner & Robert König

  2. Institute for Advanced Study, Technical University of Munich, 85748, Garching, Germany

    Robert König

  3. Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, 91125, U.S.A.

    Burak Şahinoğlu & Eugene Tang

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  1. Martina Gschwendtner
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  2. Robert König
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  3. Burak Şahinoğlu
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Correspondence to Burak Şahinoğlu.

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ArXiv ePrint: 1902.02115

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Gschwendtner, M., König, R., Şahinoğlu, B. et al. Quantum error-detection at low energies. J. High Energ. Phys. 2019, 21 (2019). https://doi.org/10.1007/JHEP09(2019)021

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  • Received: 14 June 2019

  • Accepted: 08 August 2019

  • Published: 03 September 2019

  • DOI: https://doi.org/10.1007/JHEP09(2019)021

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Keywords

  • Bethe Ansatz
  • Holography and condensed matter physics (AdS/CMT)
  • Lattice Integrable Models
  • Topological States of Matter
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