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IEEE Communications Letters

Quantum Synchronizable Codes From the Cyclotomy of Order Four

Lanqiang Li, Shixin Zhu, Li Liu

Published Oct 25, 2018• 20 citations
Publisher

Abstract

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.

DOI
10.1109/lcomm.2018.2877989

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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 (in short QSCs) are a special type of quantum error correcting codes (ECCs) which are useful to correct bit error, phase error, and misalignment in the block of synchronization. In this review paper, two classes of cyclic codes are converted into classes of QSCs. The QSCs with the greatest resistance to misalignment are Calderbank–Shor–Steane QECCs. Quantum information necessitates error correction, and quantum technologies are employed for safe communication, machine learning, and chemical analysis. Due to the non-cloning theorem, decoherence and the difficulty of measuring quantum states, quantum information processing is more challenging than classical information processing. Due to the high frequency of faults, a quantum computer needs an error detection and correction mechanism. To identify quantum information unit bounds in the absence of block synchronization, quantum information boundaries must be located using coding theory in quantum computing and communication systems and this prevents decoherence and correct errors while synchronizing qubits. Also, this method generates synchronizable and error-correcting quantum codes.
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 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.
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.