A Blindness Property of the Min-Sum Decoding for the Toric Code

Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to improving the error correction performance of the toric c...

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Vydané v:IEEE journal on selected areas in information theory Ročník 6; s. 138 - 149
Hlavní autori: Crest, Julien Du, Mhalla, Mehdi, Savin, Valentin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Piscataway IEEE 2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Algorithms
Blindness
Codes
Complexity
Computer Science
Electronic mail
Error analysis
Error correcting codes
Error correction
Fault tolerance
Fault tolerant systems
Iterative decoding
Maximum likelihood decoding
Message passing
message-passing decoding
minimum-sum algorithm
Noise
Quantum computing
Quantum error correction
Qubit
Qubits (quantum computing)
toric code
ISSN:2641-8770, 2641-8770
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Abstract Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to improving the error correction performance of the toric code under message-passing decoding, a class of low-complexity, iterative decoding algorithms that play a central role in both theory and practice of classical low-density parity-check codes. Here, we provide a theoretical analysis of the toric code under min-sum (MS) decoding, a message-passing decoding algorithm known to solve the maximum-likelihood decoding problem in a localized manner, for codes defined by acyclic graphs. Our analysis reveals an intrinsic limitation of the toric code, which confines the propagation of local information during the message-passing process. We show that if the unsatisfied checks of an error syndrome are at distance <inline-formula> <tex-math notation="LaTeX">\ge 5 </tex-math></inline-formula> from each other, then MS decoding is locally blind: the qubits in the direct neighborhood of an unsatisfied check are never aware of any other unsatisfied checks, except their direct neighbor. Moreover, we show that degeneracy is not the only cause of decoding failures for errors of weight at least 4, that is, the MS non-degenerate decoding radius is equal to 3, for any toric code of distance <inline-formula> <tex-math notation="LaTeX">\ge 9 </tex-math></inline-formula>. Finally, complementing our theoretical analysis, we present a pre-processing method of practical relevance. The proposed method, referred to as stabiliser blowup, has linear complexity and allows correcting all (degenerate) errors of weight up to 3, providing quadratic improvement in the logical error rate performance, as compared to MS alone.
AbstractList Kitaev’s toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to improving the error correction performance of the toric code under message-passing decoding, a class of low-complexity, iterative decoding algorithms that play a central role in both theory and practice of classical low-density parity-check codes. Here, we provide a theoretical analysis of the toric code under min-sum (MS) decoding, a message-passing decoding algorithm known to solve the maximum-likelihood decoding problem in a localized manner, for codes defined by acyclic graphs. Our analysis reveals an intrinsic limitation of the toric code, which confines the propagation of local information during the message-passing process. We show that if the unsatisfied checks of an error syndrome are at distance [Formula Omitted] from each other, then MS decoding is locally blind: the qubits in the direct neighborhood of an unsatisfied check are never aware of any other unsatisfied checks, except their direct neighbor. Moreover, we show that degeneracy is not the only cause of decoding failures for errors of weight at least 4, that is, the MS non-degenerate decoding radius is equal to 3, for any toric code of distance [Formula Omitted]. Finally, complementing our theoretical analysis, we present a pre-processing method of practical relevance. The proposed method, referred to as stabiliser blowup, has linear complexity and allows correcting all (degenerate) errors of weight up to 3, providing quadratic improvement in the logical error rate performance, as compared to MS alone.
Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to improving the error correction performance of the toric code under message-passing decoding, a class of low-complexity, iterative decoding algorithms that play a central role in both theory and practice of classical low-density parity-check codes. Here, we provide a theoretical analysis of the toric code under min-sum (MS) decoding, a message-passing decoding algorithm known to solve the maximum-likelihood decoding problem in a localized manner, for codes defined by acyclic graphs. Our analysis reveals an intrinsic limitation of the toric code, which confines the propagation of local information during the message-passing process. We show that if the unsatisfied checks of an error syndrome are at distance <inline-formula> <tex-math notation="LaTeX">\ge 5 </tex-math></inline-formula> from each other, then MS decoding is locally blind: the qubits in the direct neighborhood of an unsatisfied check are never aware of any other unsatisfied checks, except their direct neighbor. Moreover, we show that degeneracy is not the only cause of decoding failures for errors of weight at least 4, that is, the MS non-degenerate decoding radius is equal to 3, for any toric code of distance <inline-formula> <tex-math notation="LaTeX">\ge 9 </tex-math></inline-formula>. Finally, complementing our theoretical analysis, we present a pre-processing method of practical relevance. The proposed method, referred to as stabiliser blowup, has linear complexity and allows correcting all (degenerate) errors of weight up to 3, providing quadratic improvement in the logical error rate performance, as compared to MS alone.
Author Savin, Valentin
Mhalla, Mehdi
Crest, Julien Du
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10.22331/q-2023-06-07-1037
10.1016/B978-0-12-396499-1.00013-3
10.1109/TIT.2013.2292061
10.1016/S0003-4916(02)00018-0
10.1109/TIT.2004.839541
10.1103/PhysRevResearch.2.043423
10.1109/ITW54588.2022.9965902
10.1109/TC.2019.2948612
10.26421/qic8.10-8
10.22331/q-2024-05-02-1334
10.1038/s41586-022-05434-1
10.1109/TIT.2011.2169534
10.1103/PhysRevLett.122.200501
10.56021/9781421407944
10.1103/PhysRevA.100.012330
10.1109/TIT.2024.3396620
10.1038/s41534-022-00623-2
10.1109/jsait.2025.3571313
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References ref13
ref12
ref14
ref20
ref11
ref10
ref21
ref2
ref1
ref17
ref16
ref19
Wiberg (ref15) 1996
ref18
ref8
ref7
ref4
ref3
ref6
ref5
Yao (ref9) 2023
References_xml – ident: ref2
  doi: 10.22331/q-2021-11-22-585
– ident: ref10
  doi: 10.22331/q-2023-06-07-1037
– ident: ref16
  doi: 10.1016/B978-0-12-396499-1.00013-3
– year: 2023
  ident: ref9
  article-title: Belief propagation decoding of quantum LDPC codes with guided decimation
  publication-title: arXiv:2312.10950
– ident: ref17
  doi: 10.1109/TIT.2013.2292061
– ident: ref11
  doi: 10.1016/S0003-4916(02)00018-0
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  doi: 10.1109/TIT.2004.839541
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  doi: 10.1103/PhysRevResearch.2.043423
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  doi: 10.1109/ITW54588.2022.9965902
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  doi: 10.1109/TC.2019.2948612
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  doi: 10.26421/qic8.10-8
– ident: ref5
  doi: 10.22331/q-2024-05-02-1334
– ident: ref12
  doi: 10.1038/s41586-022-05434-1
– ident: ref6
  doi: 10.1109/TIT.2011.2169534
– ident: ref13
  doi: 10.1103/PhysRevLett.122.200501
– volume-title: Codes and decoding on general graphs
  year: 1996
  ident: ref15
– ident: ref19
  doi: 10.56021/9781421407944
– ident: ref7
  doi: 10.1103/PhysRevA.100.012330
– ident: ref20
  doi: 10.1109/TIT.2024.3396620
– ident: ref8
  doi: 10.1038/s41534-022-00623-2
– ident: ref18
  doi: 10.1109/jsait.2025.3571313
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Snippet Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity...
Kitaev’s toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity...
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SubjectTerms Algorithms
Blindness
Codes
Complexity
Computer Science
Electronic mail
Error analysis
Error correcting codes
Error correction
Fault tolerance
Fault tolerant systems
Iterative decoding
Maximum likelihood decoding
Message passing
message-passing decoding
minimum-sum algorithm
Noise
Quantum computing
Quantum error correction
Qubit
Qubits (quantum computing)
toric code
Title A Blindness Property of the Min-Sum Decoding for the Toric Code
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