Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

A family of quantum codes with performances close to the hashing bound under iterative decoding

Denise Maurice, Jean–Pierre Tillich, Iryna Andriyanova

Published Jul 1, 2013• 6 citations
Publisher

Abstract

We propose here a new construction of quantum codes combining an improved version of a family of spatially coupled quantum LDPC codes, suggested in [1], with a family of error reducing turbo-codes of [2]. This new construction displays outstanding performances under iterative decoding for noise levels very close to the hashing bound, without needing qubits, protected from noise as in [1].

DOI
10.1109/isit.2013.6620358

Related papers

Quantum turbo codes with unbounded minimum distance and excellent error-reducing performance

Mamdouh Abbara, Jean–Pierre Tillich

We construct here a new family of quantum codes related to serial turbo-codes which are excellent error-reducing codes under iterative decoding for very large channel noise values. Moreover we also show that this family of codes has unbounded minimum distance.

IEEE Information Theory Workshop (ITW)•Oct 1, 2011•3 citations

Spatially coupled quantum LDPC codes

Iryna Andriyanova, Denise Maurice, Jean–Pierre Tillich

We propose here a new construction of spatially coupled quantum LDPC codes using a small amount of entangled qubit pairs shared between the encoder and the decoder which improves quite significantly all other constructions of quantum LDPC codes or turbo-codes with the same rate.

IEEE Information Theory Workshop (ITW)•Sep 1, 2012•12 citations

Asymptotically good codes with high iterative decoding performances

Iryna Andriyanova, Jean–Pierre Tillich, Jean-Claude Carlach

We investigate a new class of codes which is in some senses a hybrid between LDPC codes and turbo-codes. We show that when the parameters of this class are well chosen they have very good iterative decoding performances and at the same time a minimum distance which is typically linear in the code length

IEEE International Symposium on Information Theory (ISIT)•Jan 1, 2005•9 citations

Quantum serial turbo-codes

David Poulin, Jean–Pierre Tillich, Harold Ollivier

We present a theory of quantum serial turbo-codes and study their performance numerically on a depolarization channel. These codes can be considered as a generalization of classical serial turbo-codes. As their classical cousins, they can be iteratively decoded and with well chosen constituent convolutional codes, we observe an important reduction of the word error rate as the number of encoded qubits increases. Our construction offers several advantages over quantum LDPC codes. First, the Tanner graph used for decoding can be chosen to be free of 4-cycles that deteriorate the performances of iterative decoding. Secondly, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice. We address two issues related to the encoding of convolutional codes that are directly relevant for turbo-codes, namely the character of being recursive and non-catastrophic. We define a quantum analogue of a state diagram that provides an efficient way to verify these properties on a given quantum convolutional encoder. Unfortunately, we also prove that all recursive quantum convolutional encoder have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be non-catastrophic and non-recursive. While the resulting families of turbo-codes have bounded minimum distance, from a pragmatic point of view the effective minimum distances of the codes that we have simulated are large enough for not degrading iterative decoding performance up to reasonable word error rates and block sizes.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2008•29 citations

Quantum serial turbo-codes

David Poulin, Jean–Pierre Tillich, Ollivier, Harold

We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First, the Tanner graph used for decoding is free of 4-cycles that deteriorate the performances of iterative decoding. Secondly, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice. We define a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular its recursiveness and the presence of catastrophic error propagation. We prove that all recursive quantum convolutional encoder have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be non-catastrophic and non-recursive. While the resulting families of turbo-codes have bounded minimum distance, from a pragmatic point of view the effective minimum distances of the codes that we have simulated are large enough not to degrade the iterative decoding performance up to reasonable word error rates and block sizes. With well chosen constituent convolutional codes, we observe an important reduction of the word error rate as the code length increases.

arXiv:0712.2888•Dec 18, 2007•3 citations

Quantum error correction near the coding theoretical bound

Daiki Komoto, Kenta Kasai

Abstract Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits1. However, many impactful applications demand quantum computations with millions of logical qubits2, necessitating highly scalable quantum error correction. In classical information theory, low-density parity-check (LDPC) codes3 can approach channel capacity efficiently4. Yet, no quantum error-correcting codes with efficient decoding have been shown to approach the hashing bound—a fundamental limit on quantum capacity—despite decades of research5–7. Here, we present quantum LDPC codes that not only approach the hashing bound but also allow decoding with computational cost linear in the number of physical qubits. This breakthrough paves the way for large-scale, fault-tolerant quantum computation. Combined with emerging hardware that manages many qubits, our approach brings quantum solutions to important real-world problems significantly closer to reality.

arXiv:2412.21171•npj Quantum Information•Sep 30, 2025•6 citations
We propose here a new construction of quantum codes combining an improved version of a family of spatially coupled quantum LDPC codes, suggested in [1], with a family of error reducing turbo-codes of [2]. This new construction displays outstanding performances under iterative decoding for noise levels very close to the hashing bound, without needing qubits, protected from noise as in [1].
We present a theory of quantum serial turbo-codes and study their performance numerically on a depolarization channel. These codes can be considered as a generalization of classical serial turbo-codes. As their classical cousins, they can be iteratively decoded and with well chosen constituent convolutional codes, we observe an important reduction of the word error rate as the number of encoded qubits increases. Our construction offers several advantages over quantum LDPC codes. First, the Tanner graph used for decoding can be chosen to be free of 4-cycles that deteriorate the performances of iterative decoding. Secondly, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice. We address two issues related to the encoding of convolutional codes that are directly relevant for turbo-codes, namely the character of being recursive and non-catastrophic. We define a quantum analogue of a state diagram that provides an efficient way to verify these properties on a given quantum convolutional encoder. Unfortunately, we also prove that all recursive quantum convolutional encoder have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be non-catastrophic and non-recursive. While the resulting families of turbo-codes have bounded minimum distance, from a pragmatic point of view the effective minimum distances of the codes that we have simulated are large enough for not degrading iterative decoding performance up to reasonable word error rates and block sizes.
We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First, the Tanner graph used for decoding is free of 4-cycles that deteriorate the performances of iterative decoding. Secondly, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice. We define a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular its recursiveness and the presence of catastrophic error propagation. We prove that all recursive quantum convolutional encoder have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be non-catastrophic and non-recursive. While the resulting families of turbo-codes have bounded minimum distance, from a pragmatic point of view the effective minimum distances of the codes that we have simulated are large enough not to degrade the iterative decoding performance up to reasonable word error rates and block sizes. With well chosen constituent convolutional codes, we observe an important reduction of the word error rate as the code length increases.
Abstract Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits1. However, many impactful applications demand quantum computations with millions of logical qubits2, necessitating highly scalable quantum error correction. In classical information theory, low-density parity-check (LDPC) codes3 can approach channel capacity efficiently4. Yet, no quantum error-correcting codes with efficient decoding have been shown to approach the hashing bound—a fundamental limit on quantum capacity—despite decades of research5–7. Here, we present quantum LDPC codes that not only approach the hashing bound but also allow decoding with computational cost linear in the number of physical qubits. This breakthrough paves the way for large-scale, fault-tolerant quantum computation. Combined with emerging hardware that manages many qubits, our approach brings quantum solutions to important real-world problems significantly closer to reality.