Quantum Synchronizable Codes on Sextic Cyclotomy
Tao Wang, Tongjiang Yan, Xueting Wang
TL;DR
This paper introduces new quantum synchronizable codes based on sextic cyclotomic classes that achieve optimal synchronization bounds and exhibit strong error correction for quantum noise and misalignment.
Contribution
The paper constructs two classes of CSS quantum synchronizable codes using sextic cyclotomic cyclic codes, reaching the upper bound of synchronization capability.
Findings
Codes reach the upper bound of synchronization.
Codes have good error-correcting capabilities.
Codes are based on optimal or near-optimal cyclic codes.
Abstract
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.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Quantum Information and Cryptography