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IEEE Communications Letters

A New Family of Quantum Synchronizable Codes

Xia Li, Qin Yue

Published Sep 30, 2020• 10 citations
Publisher

Abstract

Quantum synchronizable codes (QSCs) are special quantum error-correcting codes that correct the effects of both quantum noise on qubits and misalignment in block synchronization. In this letter, we construct a family of QSCs from cyclic codes. The best attainable misalignment tolerance can also be achieved under certain constraints. And we give two classes of specific constructions of QSCs, which achieve the best attainable misalignment tolerance. Moreover, the second class of QSCs possess good error-correcting capability towards bit errors and phase errors.

DOI
10.1109/lcomm.2020.3027803

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Quantum synchronizable codes (QSCs) are special quantum error-correcting codes that correct the effects of both quantum noise on qubits and misalignment in block synchronization. In this letter, we construct a family of QSCs from cyclic codes. The best attainable misalignment tolerance can also be achieved under certain constraints. And we give two classes of specific constructions of QSCs, which achieve the best attainable misalignment tolerance. Moreover, the second class of QSCs possess good error-correcting capability towards bit errors and phase errors.
Quantum synchronizable codes (QSCs) are special quantum error-correcting codes (QECCs) that correct the effects of both quantum noise on qubits and misalignment in block synchronization. In this letter, we construct two classes of QSCs from the cyclic codes which are obtained by the cyclotomic classes of order four. The QSCs constructed are Calderbank-Shor-Steane QECCs which can tolerate maximum number of misalignment errors. Moreover, the QSCs usually possess good error-correcting capability towards bit error and phase error, due to many cyclic codes employed to construct QSCs are optimal or almost optimal.
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, a new method for construct quantum synchronizable codes from negacyclic codes are proposed, where the length of these negacyclic codes are ppp and pqpqpq. Through this method, the quantum synchronizable code possesses optimal or almost optimal error-correcting capability towards bits errors and phase errors, since the negacyclic codes we used are optimal or almost optimal. Moreover, this paper contributes to construct two classes quantum synchronizable codes, whose synchronization capabilities can reach the upper limit under certain conditions.
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, the quantum synchronizable codes constructed are CSS quantum error-correcting codes whose synchronization capabilities reach the upper bound. And we use cyclic codes gained by sextic cyclotomic classes to construct two classes of quantum synchronizable codes. Moreover, the quantum synchronizable codes are posses good error-correcting capability towards bit error and phase error, since the cyclic codes we used are optimal or almost optimal.
Quantum synchronizable codes (QSCs) are designed to correct both Pauli errors and synchronization misalignment. In this letter, we introduce a new framework for constructing QSCs based on classical coset codes. This construction is versatile, yielding codes for both random and, notably, burst errors, thereby extending the scope of existing QSC designs. The resulting codes exhibit two notable properties: they fully preserve the phase-error-correction capability of their parent Calderbank-Shor-Steane (CSS) codes, and in the absence of misalignment, they revert to the full error-correcting power of the parent codes.
Quantum Synchronizable Codes From Cyclotomic Classes of Order Two over Z2q\mathbb{Z}_{2q}Z2q​
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over Z2q\mathbb{Z}_{2q}Z2q​, whose synchronization capabilities can reach the upper bound under certain conditions. Moreover, the quantum synchronizable codes possess good error-correcting capability towards bit errors and phase errors.
A class of quantum synchronizable codes of length 2n2^n2n over Fq{\rm F}_qFq​
Quantum synchronizable codes (QSCs) are special quantum error-correcting codes which can be used to correct the effects of quantum noise on qubits and misalignment in block synchronization. In this paper, a new class of quantum synchronizable codes of length 2n2^n2n are constructed by using the cyclotomic cosets, whose synchronization capabilities always reach the upper bound 2n2^n2n.