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Cited by 486Quantum Computing Algorithms and ArchitectureQuantum many-body systemsQuantum Information and Cryptography

Operator quantum error-correcting subsystems for self-correcting quantum memories

Open access
Bacon, Dave·2006·Physical Review A
DOI 10.1103/physreva.73.012340
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Abstract

The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum error-correcting codes, one requires the ability to apply a procedure which exactly reverses on the error-correcting subspace any correctable error. In contrast, for operator error-correcting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform corrections only modulo the subsystem structure. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator error-correcting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is self-correcting. Such a system will be a natural high-temperature quantum memory, robust to noise without external intervening quantum error-correction procedures.

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  • The Bacon-Shor code is the canonical example of a subsystem code, defined on an M×N rectangular lattice of qubits.

    “The Bacon–Shor code [109] is the canonical example of a subsystem code, defined on an M ×N rectangular lattice of qubits.”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [109]

    Section IV (p. 3) presents a two-dimensional subsystem code, and Section B (p. 6) explicitly calls its encoding a subsystem encoding. But Section A (p. 3) defines the qubits on an n × n square lattice, not the general M × N rectangular lattice specified in the claim. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • Depending on the scheme being used, typically between 7 and 9 physical qubits are needed to represent the state of one qubit.

    “Depending on the scheme being used, typically between 7 [55] and 9 [56][57][58] physical qubits are needed to represent the state of one qubit.”

    From Neutral atom quantum computing hardware: performance and end-user perspective (2023) · cites this paper as [56]

  • Any physically allowed super-operator from k to l qubits can be described as a combination of adding k+l blank qubits, applying a unitary transformation on the 2k+l qubits, and then tracing out 2k qubits.

    “A lemma by Choi[16], and Hellwig and Kraus[45] asserts that any physically allowed super-operator from k to l qubits can be described as a combination of the above three operations: add k + l blank qubits, apply a unitary transformation on the 2 k + l qubits and then trace out 2 k qubits.”

    From Fault-Tolerant Quantum Computation with Constant Error Rate (2008) · cites this paper as [16]

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Cites

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Research works printed but not linked: 25

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Authors
Bacon, D.
Affiliations
University of Washington (US)
Corresponding author
Bacon, Dave
ORCID
Bacon, Dave
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2006-01-30
Volume
73
Issue
1
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.73.012340
OpenAlex
W1999770545
Cited by
486
References
4
Citations by year
2026: 17 · 2025: 35 · 2024: 35 · 2023: 36 · 2022: 23 · 2021: 24 · 2020: 23 · 2019: 23 · 2018: 17 · 2017: 21 · 2016: 15 · 2015: 13 · 2014: 18 · 2013: 40 · 2012: 30
FWCI
27.77
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
self-correcting quantum memory, quantum memory, local Hamiltonians, square lattice, cubic lattice, mean-field theory, subspace codes

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