Degenerate asymmetric quantum concatenated codes for correcting biased quantum errors
Ji-Hao Fan(樊继豪)1,†, Jun Li(李骏)1,‡, Han-Wu Chen(陈汉武)2, and Wen-Jie Liu(刘文杰)3
1 School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; 2 School of Computer Science and Engineering, Southeast University, Nanjing 211189, China; 3 School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing 210044, China
Abstract In most practical quantum mechanical systems, quantum noise due to decoherence is highly biased towards dephasing. The quantum state suffers from phase flip noise much more seriously than from the bit flip noise. In this work, we construct new families of asymmetric quantum concatenated codes (AQCCs) to deal with such biased quantum noise. Our construction is based on a novel concatenation scheme for constructing AQCCs with large asymmetries, in which classical tensor product codes and concatenated codes are utilized to correct phase flip noise and bit flip noise, respectively. We generalize the original concatenation scheme to a more general case for better correcting degenerate errors. Moreover, we focus on constructing nonbinary AQCCs that are highly degenerate. Compared to previous literatures, AQCCs constructed in this paper show much better parameter performance than existed ones. Furthermore, we design the specific encoding circuit of the AQCCs. It is shown that our codes can be encoded more efficiently than standard quantum codes.
(Quantum error correction and other methods for protection against decoherence)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61802175, 61871120, 61872184, and 62071240) and the Fundamental Research Funds for the Central Universities, China (Grant No. NZ2020021).
Corresponding Authors:
Ji-Hao Fan, Jun Li
E-mail: jihao.fan@outlook.com;jun.li@njust.edu.cn
Cite this article:
Ji-Hao Fan(樊继豪), Jun Li(李骏), Han-Wu Chen(陈汉武), and Wen-Jie Liu(刘文杰) Degenerate asymmetric quantum concatenated codes for correcting biased quantum errors 2021 Chin. Phys. B 30 120302
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