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NLTS Hamiltonians from Good Quantum Codes

Authors:

Nikolas P. Breuckmann,

Chinmay NirkheAuthors Info & Claims

STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of Computing

Pages 1090 - 1096

https://doi.org/10.1145/3564246.3585114

Published: 02 June 2023 Publication History

Editorial Notes

The authors have requested minor, non-substantive changes to the VoR and, in accordance with ACM policies, a Corrected VoR was published on August 21, 2024. For reference purposes the VoR may still be accessed via the Supplemental Material section on this page.

Abstract

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the state). We prove this conjecture by showing that a particular family of constant-rate and linear-distance qLDPC codes correspond to NLTS local Hamiltonians, although we believe this to be true for all current constructions of good qLDPC codes.

Supplementary Material

3585114-vor (3585114-vor.pdf)

Version of Record for "HNLTS Hamiltonians from Good Quantum Codes" by Anshu et al., Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023).

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Cited By

Anschuetz EGamarnik DKiani B(2024)Combinatorial NLTS From the Overlap Gap PropertyQuantum10.22331/q-2024-11-19-15278(1527)Online publication date: 19-Nov-2024
https://doi.org/10.22331/q-2024-11-19-1527
Cross AHe ZNatarajan ASzegedy MZhu G(2024)Quantum Locally Testable Code with Constant SoundnessQuantum10.22331/q-2024-10-18-15018(1501)Online publication date: 18-Oct-2024
https://doi.org/10.22331/q-2024-10-18-1501
Bentsen GNguyen PSwingle B(2024)Approximate Quantum Codes From Long WormholesQuantum10.22331/q-2024-08-14-14398(1439)Online publication date: 14-Aug-2024
https://doi.org/10.22331/q-2024-08-14-1439
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Index Terms

NLTS Hamiltonians from Good Quantum Codes
1. Theory of computation
  1. Computational complexity and cryptography
    1. Quantum complexity theory
  2. Models of computation
    1. Quantum computation theory
      1. Quantum information theory

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Published In

cover image ACM Conferences

STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of Computing

June 2023

1926 pages

ISBN:9781450399135

DOI:10.1145/3564246

General Chair:
Barna Saha
University of California at San Diego, USA
,
Program Chair:
Rocco A. Servedio
Columbia University, USA

Copyright © 2023 ACM.

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Published: 02 June 2023

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EPSRC Prosperity Partnership in Quantum Software for Simulation and Modelling

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June 20 - 23, 2023

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https://doi.org/10.22331/q-2024-11-19-1527
Cross AHe ZNatarajan ASzegedy MZhu G(2024)Quantum Locally Testable Code with Constant SoundnessQuantum10.22331/q-2024-10-18-15018(1501)Online publication date: 18-Oct-2024
https://doi.org/10.22331/q-2024-10-18-1501
Bentsen GNguyen PSwingle B(2024)Approximate Quantum Codes From Long WormholesQuantum10.22331/q-2024-08-14-14398(1439)Online publication date: 14-Aug-2024
https://doi.org/10.22331/q-2024-08-14-1439
Natarajan ANirkhe C(2024)A distribution testing oracle separation between QMA and QCMAQuantum10.22331/q-2024-06-17-13778(1377)Online publication date: 17-Jun-2024
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