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International Workshop on Signal Design and its Applications in Communications

Quantum Synchronizable Codes from Generalized Cyclotomy

Xueting Wang, Tongjiang Yan, Tao Wang, Shiwen Sun

Published Aug 1, 2022• 2 citations
Publisher

Abstract

Quantum synchronizable codes can correct the ef-fects of quantum noise on qubits as well as misalignment in block synchronization. In this paper, dual-containing cyclic codes of length$2pq$and$p^{2}$are constructed by generalized cyclotomy, where some of the cyclic codes of length$p^{2}$are optimal or almost optimal. Based on these cyclic codes and their augmented codes, we obtain two new classes of quantum synchronizable codes whose synchronization capabilities are the best.

DOI
10.1109/iwsda50346.2022.9870598

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Quantum synchronizable codes can correct the ef-fects of quantum noise on qubits as well as misalignment in block synchronization. In this paper, dual-containing cyclic codes of length2pq2pq2pqandp2p^{2}p2are constructed by generalized cyclotomy, where some of the cyclic codes of lengthp2p^{2}p2are optimal or almost optimal. Based on these cyclic codes and their augmented codes, we obtain two new classes of quantum synchronizable codes whose synchronization capabilities are the best.
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 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 (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 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 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.