arXiv:2110.13659

A class of quantum synchronizable codes of length $2^n$ over ${\rm F}_q$

Shiwen Sun, Tongjiang Yan, Yuhua Sun, Tao Wang, Xueting Wang

Published Oct 25, 2021• 0 citations

Abstract

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 $2^n$ are constructed by using the cyclotomic cosets, whose synchronization capabilities always reach the upper bound $2^n$.

DOI: 10.48550/arxiv.2110.13659

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arXiv:2110.13659

A class of quantum synchronizable codes of length $2^n$ over ${\rm F}_q$ A class of quantum synchronizable codes of length $2^n$ over ${\rm F}_q$

Shiwen Sun, Tongjiang Yan, Yuhua Sun, Tao Wang, Xueting Wang

Published Oct 25, 2021• 0 citations

arXiv HTML PDF

Abstract

2^n

are constructed by using the cyclotomic cosets, whose synchronization capabilities always reach the upper bound

2^n

DOI: 10.48550/arxiv.2110.13659

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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 $\mathbb{Z}_{2q}$ , 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.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 $\mathbb{Z}_{2q}$, 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.

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A class of quantum synchronizable codes of length

2^n

over

{\rm F}_q

2^n

are constructed by using the cyclotomic cosets, whose synchronization capabilities always reach the upper bound

2^n

Quantum Synchronizable Codes From Cyclotomic Classes of Order Two over

\mathbb{Z}_{2q}

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

\mathbb{Z}_{2q}

, 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.

p

and

pq

. 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 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.