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Quantum error-detection at low energies

Gschwendtner, Martina and König, Robert and Şahinoğlu, Burak and Tang, Eugene (2019) Quantum error-detection at low energies. Journal of High Energy Physics, 2019 (9). Art. No. 21. ISSN 1029-8479.

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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(n^(1−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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Additional Information:© 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: June 14, 2019; Accepted: August 8, 2019; Published: September 3, 2019. We thank Ahmed Almheiri, Fernando Brandão, Elizabeth Crosson, Spiros Michalakis, and John Preskill for discussions. We thank the Kavli Institute for Theoretical Physics for their hospitality as part of a follow-on program, as well as the coordinators of the QINFO17 program, where this work was initiated; this research was supported in part by the National Science Foundation under Grant No. PHY-1748958. RK acknowledges support by the Technical University of Munich - Institute of Advanced Study, funded by the German Excellence Initiative and the European Union Seventh Framework Programme under grant agreement no. 291763 and by the German Federal Ministry of Education through the funding program Photonics Research Germany, contract no. 13N14776 (QCDA-QuantERA). BS acknowledges the support from the Simons Foundation through It from Qubit collaboration; this work was supported by a grant from the Simons Foundation/SFARI (385612, JPP). ET acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), PGSD3-502528-2017. BS and ET also acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant No. PHY-1733907).
Group:UNSPECIFIED, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Technical University of MunichUNSPECIFIED
German Excellence InitiativeUNSPECIFIED
European Research Council (ERC)291763
Bundesministerium für Bildung und Forschung (BMBF)13N14776
Simons Foundation385612
Natural Sciences and Engineering Research Council of Canada (NSERC)PGSD3-502528-2017
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Subject Keywords:Bethe Ansatz; Holography and condensed matter physics (AdS/CMT); Lattice Integrable Models; Topological States of Matter
Issue or Number:9
Record Number:CaltechAUTHORS:20190905-141023968
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Official Citation:Gschwendtner, M., König, R., Şahinoğlu, B. et al. J. High Energ. Phys. (2019) 2019: 21.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98438
Deposited By: Tony Diaz
Deposited On:05 Sep 2019 21:32
Last Modified:04 Jun 2020 10:14

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