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

Communications in Theoretical Physics

A Construction of Quantum Error-Locating Codes*

Jihao Fan, Hanwu Chen

Published Jan 1, 2017• 2 citations
Publisher

Abstract

Abstract We present the construction of quantum error-locating (QEL) codes based on classical error-locating (EL) codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum error-detecting codes. Then QEL codes can locate qubit errors within one sub-block of the received qubit symbols but do not need to determine the exact locations of the erroneous qubits. We show that, an e-error-locating code derived from an arbitrary binary cyclic code with generator polynomial g ( x ) , can lead to a QEL code with e error-locating abilities, only if g ( x ) does not contain the ( 1 + x ) -factor .

DOI
10.1088/0253-6102/67/1/37

Related papers

Quantum Error Source and Channel Coding

Dennis G. Lucarelli

Quantum error correction draws many of its principles and constructions from classical coding theory, adapted to the unique aspects of quantum mechanics. Here we extend this correspondence to a block of logical qubits, each prepared in the same quantum code, by coupling the block through a classical error correcting code: syndrome qubits then carry error information from several logical qubits at once, and collective inference recovers the errors. Algebraically, the construction defines subgroups of the product stabilizer group corresponding to duals of classical codes, and we prove that a lookup table decoder corrects every error pattern respecting the correction radii of the two constituent codes. For classical algebraic code families, the number of syndrome qubits serving $L$ logical qubits scales as ${\cal O}(\log_2(L+1))$ at the code-capacity level, though at the price of stabilizer weight growing with the block length. An entropy bound shows that check weights need not grow with $L$. Under a phenomenological noise model, the same lookup table identifies measurement errors by nearest-neighbor post-processing, and classical algebraic decoders locate exactly the logical qubits carrying errors even with noisy syndromes. More broadly, we argue that quantum error correction, reduced to its functional core, is source compression in the sense of Shannon, whose source and channel coding theorems bound the overhead rates of quantum post-selection tasks.

arXiv:2004.09479•Apr 20, 2020•0 citations

Constructing Asymmetric Quantum and Subsystem Cyclic Codes

Salah A. Aly

Abstract. It is recently conjectured in quantum information processing that phase-shift errors occur with high probability than qubit-flip errors, hence the former is more disturbing to quantum information than the later one. This leads us to construct asymmetric quantum error controlling codes to protect quantum information over asymmetric channels, Pr Z ≥ Pr X. In this paper we present two generic methods to derive asymmetric quantum cyclic codes using the generator polynomials and defining sets of classical cyclic codes. Consequently, the methods allow us to construct several families of asymmetric quantum BCH, RS, and RM codes. Finally, the methods are used to construct families of asymmetric subsystem codes. 1

arXiv:0906.5339•Jun 29, 2009•0 citations

Quantum Event-Error Detection Codes

Ying Guo, Guihua Zeng

To simultaneously detect random and burst quantum errors which may be generalized as quantum event errors, a quantum error detection code, called the quantum event-error detection code, is first investigated in analogy to the classical event-error detection code. The proposed code can be used to detect the length, number and location of errors occurring in every error event. Two special quantum event-error detection codes are constructed by exploiting different approaches according to the derived syndrome, and their number-bound of generators of the stabilizer is also derived. Finally, the proposed theory on the quantum event-error detection code for quantum single-event error is extended to a more general case, i.e., the quantum composite-event error, so that the general quantum event-error detection code can be constructed.

Journal of the Physical Society of Japan•Nov 15, 2005•8 citations

Existence of quantum event-error detecting code

Ying Guo, Guihua Zeng, Fucheng Zhu

A novel quantum detection code is first proposed, analogous to the classic event-error detection code, which can detect simultaneously random and burst quantum errors. The proposed code, called quantum event-error detection code, can detect the length, number and location of the quantum errors in every listed quantum error event. Especially, two kinds of quantum event-error detection codes are constructed. To construct the optimal quantum event-error detection code, the number-bound of the stabilizer generators is investigated.

International Conference on Communications, Circuits and Systems•Aug 16, 2005•0 citations

A construction method for a family of quantum cyclic codes

Xinmei Wang

The problem of finding stabilizer quantum-error-correcting codes can be transformed into the problem of finding classical self-orthogonal linear codes over the Galois field GF(4) under a Hermitian inner product.A classical cyclic code over the field GF(4) is self-orthogonal with respect to the Hermitian inner product iff the generator polynomial of its dual code is a factor of its generator polynomial.Based on this connection,a class of quantum cyclic codes is constructed by finding corresponding classical cyclic codes.Some examples are also given in detail.

Journal of Xidian University•Jan 1, 2007•0 citations

On quantum tensor product codes

Jihao Fan, Yonghui Li, Min-Hsiu Hsieh +1 more

We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is constructed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs can be obtained. By selecting different types of component codes, the proposed method enables the construction of a large family of QTPCs and they can provide a wide variety of quantum error control abilities. In particular, if one of the component codes is selected as a burst-error-correction code, then QTPCs have quantum multiple-burst-error-correction abilities, provided these bursts fall in distinct subblocks. Compared with concatenated quantum codes (CQC), the component code selections of QTPCs are much more flexible than those of CQCs since only one of the component codes of QTPCs needs to satisfy the dual-containing restriction. We show that it is possible to construct QTPCs with parameters better than other classes of quantum error-correction codes (QECC), e.g., CQCs and quantum BCH codes. Many QTPCs are obtained with parameters better than previously known quantum codes available in the literature. Several classes of QTPCs that can correct multiple quantum bursts of errors are constructed based on reversible cyclic codes and maximum-distance-separable (MDS) codes.

arXiv:1605.09598•Quantum Information and Computation•Nov 1, 2017•16 citations
Abstract We present the construction of quantum error-locating (QEL) codes based on classical error-locating (EL) codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum error-detecting codes. Then QEL codes can locate qubit errors within one sub-block of the received qubit symbols but do not need to determine the exact locations of the erroneous qubits. We show that, an e-error-locating code derived from an arbitrary binary cyclic code with generator polynomial g ( x ) , can lead to a QEL code with e error-locating abilities, only if g ( x ) does not contain the ( 1 + x ) -factor .
Quantum error correction draws many of its principles and constructions from classical coding theory, adapted to the unique aspects of quantum mechanics. Here we extend this correspondence to a block of logical qubits, each prepared in the same quantum code, by coupling the block through a classical error correcting code: syndrome qubits then carry error information from several logical qubits at once, and collective inference recovers the errors. Algebraically, the construction defines subgroups of the product stabilizer group corresponding to duals of classical codes, and we prove that a lookup table decoder corrects every error pattern respecting the correction radii of the two constituent codes. For classical algebraic code families, the number of syndrome qubits serving LLL logical qubits scales as O(log⁡2(L+1)){\cal O}(\log_2(L+1))O(log2​(L+1)) at the code-capacity level, though at the price of stabilizer weight growing with the block length. An entropy bound shows that check weights need not grow with LLL. Under a phenomenological noise model, the same lookup table identifies measurement errors by nearest-neighbor post-processing, and classical algebraic decoders locate exactly the logical qubits carrying errors even with noisy syndromes. More broadly, we argue that quantum error correction, reduced to its functional core, is source compression in the sense of Shannon, whose source and channel coding theorems bound the overhead rates of quantum post-selection tasks.
Abstract. It is recently conjectured in quantum information processing that phase-shift errors occur with high probability than qubit-flip errors, hence the former is more disturbing to quantum information than the later one. This leads us to construct asymmetric quantum error controlling codes to protect quantum information over asymmetric channels, Pr Z ≥ Pr X. In this paper we present two generic methods to derive asymmetric quantum cyclic codes using the generator polynomials and defining sets of classical cyclic codes. Consequently, the methods allow us to construct several families of asymmetric quantum BCH, RS, and RM codes. Finally, the methods are used to construct families of asymmetric subsystem codes. 1
To simultaneously detect random and burst quantum errors which may be generalized as quantum event errors, a quantum error detection code, called the quantum event-error detection code, is first investigated in analogy to the classical event-error detection code. The proposed code can be used to detect the length, number and location of errors occurring in every error event. Two special quantum event-error detection codes are constructed by exploiting different approaches according to the derived syndrome, and their number-bound of generators of the stabilizer is also derived. Finally, the proposed theory on the quantum event-error detection code for quantum single-event error is extended to a more general case, i.e., the quantum composite-event error, so that the general quantum event-error detection code can be constructed.
A novel quantum detection code is first proposed, analogous to the classic event-error detection code, which can detect simultaneously random and burst quantum errors. The proposed code, called quantum event-error detection code, can detect the length, number and location of the quantum errors in every listed quantum error event. Especially, two kinds of quantum event-error detection codes are constructed. To construct the optimal quantum event-error detection code, the number-bound of the stabilizer generators is investigated.
The problem of finding stabilizer quantum-error-correcting codes can be transformed into the problem of finding classical self-orthogonal linear codes over the Galois field GF(4) under a Hermitian inner product.A classical cyclic code over the field GF(4) is self-orthogonal with respect to the Hermitian inner product iff the generator polynomial of its dual code is a factor of its generator polynomial.Based on this connection,a class of quantum cyclic codes is constructed by finding corresponding classical cyclic codes.Some examples are also given in detail.
We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is constructed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs can be obtained. By selecting different types of component codes, the proposed method enables the construction of a large family of QTPCs and they can provide a wide variety of quantum error control abilities. In particular, if one of the component codes is selected as a burst-error-correction code, then QTPCs have quantum multiple-burst-error-correction abilities, provided these bursts fall in distinct subblocks. Compared with concatenated quantum codes (CQC), the component code selections of QTPCs are much more flexible than those of CQCs since only one of the component codes of QTPCs needs to satisfy the dual-containing restriction. We show that it is possible to construct QTPCs with parameters better than other classes of quantum error-correction codes (QECC), e.g., CQCs and quantum BCH codes. Many QTPCs are obtained with parameters better than previously known quantum codes available in the literature. Several classes of QTPCs that can correct multiple quantum bursts of errors are constructed based on reversible cyclic codes and maximum-distance-separable (MDS) codes.