|
|
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.
|
Received: 12 April 2021
Revised: 14 May 2021
Accepted manuscript online: 27 May 2021
|
PACS:
|
03.67.Lx
|
(Quantum computation architectures and implementations)
|
|
03.67.Pp
|
(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
|
[1] Tang G Z, Sun S H and Li C Y 2020 Chin. Phys. Lett. 36 070301 [2] Tian Y L, Feng T F and Zhou X Q 2019 Acta Phys. Sin. 68 110302 (in Chinese) [3] Cheng X, Zhao Y C, Y C Wu and Guo G P 2021 Chin. Phys. Lett. 38 030302 [4] Ketkar A, Klappenecker A, Kumar S and Sarvepalli P K 2006 IEEE Trans. Inf. Theory 52 4892 [5] Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge:Cambridge University) pp. 426-510 [6] Dumer I, Kovalev A A and Pryadko L P 2015 Phys. Rev. Lett. 115 050502 [7] Sarvepalli P K, Klappenecker A and Rötteler M 2009 Roy. Soc. A 465 1645 [8] Tuckett D K, Darmawan A S, Chubb C T, Bravyi S, Bartlett S D and Flammia S T 2019 Phys. Rev. X 9 041031 [9] Ezerman M F, Jitman S, Kiah H M and Ling S 2013 Int. J. Quantum Inf. 11 1350027 [10] Wang L, Feng K, Ling S and Xing C P 2010 IEEE Trans. Inf. Theory 56 2938 [11] Galindo C, Geil O, Hernando F and Ruano D 2017 IEEE Trans. Inf. Theory 64 2444 [12] Christensen R B and Geil O 2020 Finite Fields Appl. 68 101742 [13] Aliferis P and Preskill J 2008 Phys. Rev. A 78 052331 [14] Brooks P and Preskill J 2013 Phys. Rev. A 87 032310 [15] Tuckett D K, Bartlett S D and Flammia S T 2018 Phys. Rev. Lett. 120 050505 [16] Tuckett D K, Bartlett S D, Flammia S T and Brown B J 2020 Phys. Rev. Lett. 124 130501 [17] Nadkarni P J and Garani S S 2017 Proceedings of the 2017 IEEE Information Theory Workshop, November 6-10, Kaohsiung, Taiwan, p. 219 [18] Nadkarni P J and Garani S S 2020 IEEE Trans. Quantum Eng. 1 2101417 [19] Lin S and Costello D J 2004 Error Control Coding:Fundamentals and Applications (New Jersey:Prentice-Hall) p. 739 [20] Fan J H, Li J, Wang J X, Wei Z H and Hsieh M H 2021 IEEE Trans. Commun. 69 3971 [21] Christandl M and Müller-Hermes A 2021 Proceedings of the 24rd Annual Conference on Quantum Information Processing, February 1-5, 2021, Munchen, Germany, p. 233, arXiv:2009.07161 [22] Ezerman M F, Jitman S, Ling S and Pasechnik D V 2013 IEEE Trans. Inf. Theory 59 6732 [23] Calderbank A R and Shor P W 1996 Phys. Rev. A 54 1098 [24] MacWilliams F J and Sloane N J A 1981 The Theory of Error-Correcting Codes (Amsterdam:North-Holland 1981) p. 93 [25] Maucher J, Zyablov V V and Bossert M 2000 IEEE Trans. Inf. Theory 46 642 [26] Guardia G G La 2012 Quantum Inf. Process. 11 591 [27] Guardia G G La 2014 Int. J. Theor. Phys. 53 2312 [28] Grassl M 2007 Bounds on the minimum distance of linear codes and quantum codes, Online available at http://www.codetables.de, 2007 [29] Ezerman M F, Ling S and Sole P 2011 IEEE Trans. Inf. Theory 57 5536 [30] Ashikhmin A, Litsyn S and Tsfasman M A 2001 Phys. Rev. A 63 032311 [31] Gottesman D 1996 Phys. Rev. A 54 1862 [32] Grassl M, Beth T and Rötteler M 2004 Int. J. Quantum Inf. 2 55 [33] Zhu X Y, Tu T, Guo A L, Zhou Z Q and Guo G C 2020 Chin. Phys. Lett. 37 020302 [34] Gong B, Tu T, Guo A L, Zhu L T and Li C F 2021 Chin. Phys. Lett. 38 044201 |
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|