Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design

doi:10.1088/1674-1056/28/1/010304

中国物理B ›› 2019, Vol. 28 ›› Issue (1): 10304-010304.doi: 10.1088/1674-1056/28/1/010304

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design

Linxi Zhang(张林曦), Changhua Zhu(朱畅华), Changxing Pei(裴昌幸)

1 State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China;
2 Science and Technology on Communication Networks Laboratory, Shijiazhuang 050081, China

收稿日期:2018-07-09 修回日期:2018-11-04 出版日期:2019-01-05 发布日期:2019-01-05
通讯作者: Linxi Zhang E-mail:zhanglinxi@stu.xidian.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61372076 and 61701375), the 111 Project, China (Grant No. B08038), the Key Research and Development Plan of Shannxi Province, China (Grant No. BBD24017290001), and the Foundation of Science and Technology on Communication Networks Laboratory, China (Grant No. KX172600031).

Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design

Linxi Zhang(张林曦)^1,2, Changhua Zhu(朱畅华)¹, Changxing Pei(裴昌幸)¹

1 State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China;
2 Science and Technology on Communication Networks Laboratory, Shijiazhuang 050081, China

Received:2018-07-09 Revised:2018-11-04 Online:2019-01-05 Published:2019-01-05
Contact: Linxi Zhang E-mail:zhanglinxi@stu.xidian.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61372076 and 61701375), the 111 Project, China (Grant No. B08038), the Key Research and Development Plan of Shannxi Province, China (Grant No. BBD24017290001), and the Foundation of Science and Technology on Communication Networks Laboratory, China (Grant No. KX172600031).

摘要/Abstract

摘要：

We propose a method to estimate the average fidelity using the unitary 2t-design of a twirled noisy channel, which is suitable for large-scale quantum circuits. Compared with the unitary 2-design in randomized benchmarking, the unitary 2t-design for the twirling of noisy channels is more flexible in construction and can provide more information. In addition, we prove that the proposed method provides an efficient and reliable estimation of the average fidelity in benchmarking multistage quantum gates and estimating the weakly gate- and time-dependent noise. For time-dependent noise, we provide a scheme of moment superoperator to analyze the noise in different experiments. In particular, we give a lower bound on the average fidelity of a channel with imperfect implementation of benchmarking and state preparation and measurement errors (SPAM).

关键词: quantum channel, average fidelity, unitary 2t-design

Abstract:

Key words: quantum channel, average fidelity, unitary 2t-design

中图分类号: (State reconstruction, quantum tomography)

03.65.Wj

03.67.Lx (Quantum computation architectures and implementations)

张林曦, 朱畅华, 裴昌幸. Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design[J]. 中国物理B, 2019, 28(1): 10304-010304.

Linxi Zhang(张林曦), Changhua Zhu(朱畅华), Changxing Pei(裴昌幸). Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design[J]. Chin. Phys. B, 2019, 28(1): 10304-010304.

参考文献 37

[1]	Lidar D and Brunn T 2013 Quantum Error Correction (Cambridge:Cambridge University Press) pp. 142-157
[2]	Aliferis P, Gottesman D and Preskill J 2005 Quantum Info. Comput. 6 97
[3]	Kueng R, Long D M, Doherty A C and Flammia S T 2016 Phys. Rev. Lett. 117 170502 doi: 10.1103/PhysRevLett.117.170502
[4]	D’Ariano G M, Paris M G A and Sacchi M F 2003 Advances in Imaging and Electron Physics 128 205 doi: 10.1016/S1076-5670(03)80065-4
[5]	Artiles L M, Gill R D and Guta M I Journal of Royal Statistical Society 2004 Journal of Royal Statistical Society 67 109
[6]	Poyatos J F, Cirac J I and Zoller P 1997 Phys. Rev. Lett. 78 390 doi: 10.1103/PhysRevLett.78.390
[7]	Wei S J, Xin T and Long G L 2018 Sci. China-Phys. Mech. Astron. 61 070311 doi: 10.1007/s11433-017-9181-9
[8]	Horodecki M, Horodecki P and Horodecki R 1998 Phys. Rev. A 60 1888
[9]	Xu Y Y, Zhou F, Chen L, Xie Y, Xue P and Feng M 2012 Chin. Phys. B 21 040304 doi: 10.1088/1674-1056/21/4/040304
[10]	Wu W, Liu X and Wang C 2018 Chin. Phys. B 27 060302 doi: 10.1088/1674-1056/27/6/060302
[11]	Chen N, Quan D X, Xu F F, Yang H and Pei C X 2015 Chin. Phys. B 24 100307 doi: 10.1088/1674-1056/24/10/100307
[12]	Blume-Kohout R, Gamble J K, Nielsen E, Rudinger K, Mizrahi J, Fortier K and Maunz P 2017 Nat. Commun. 8 14485
[13]	Merkel S T, Gambetta J M, Smolin J A, Poletto S, Corcoles A D, Johnson B R, Ryan C A and Steffen M 2013 Phys. Rev. A 87 062119 doi: 10.1103/PhysRevA.87.062119
[14]	Knill E, Leibfried D, Reichle R, Ulm U, Britton J, Blakestad R B, Jost J D, Langer C, Ozeri R, Seidelin S and Wineland D J 2007 Phys. Rev. A 77 012307
[15]	Magesan E, Gambetta J M and Emerson J 2010 Phys. Rev. Lett. 106 180504
[16]	Gaebler J P, Meier A M, Tan T R, Bowler R, Lin Y, Hanneke D, Jost J D, Home J P, Knill E, Leibfried D and Wineland D J 2012 Phys. Rev. Lett. 108 260503 doi: 10.1103/PhysRevLett.108.260503
[17]	Magesan E, Gambetta J M, Johnson B R, Ryan C A, Chow J M, Merkel S T, Silva M P, Keefe G A, Rothwell M B, Ohki T A, Ketchen M B and Steffen M 2012 Phys. Rev. Lett. 109 080505 doi: 10.1103/PhysRevLett.109.080505
[18]	Magesan E, Gambetta J M, Emerson J 2012 Phys. Rev. A 85 042311 doi: 10.1103/PhysRevA.85.042311
[19]	Wallman J J and Flammia S T 2014 New J. Phys. 16 103032 doi: 10.1088/1367-2630/16/10/103032
[20]	Wallman J J, Barnhill M, Emerson J 2016 New J. Phys. 18 043021 doi: 10.1088/1367-2630/18/4/043021
[21]	Wallman J J and Emerson J 2016 Phys. Rev. A 94 052325 doi: 10.1103/PhysRevA.94.052325
[22]	Helsen J, Wallman J J, Flammia S T and Wehner S 2017 arXiv:1701.04299v1 [quant-ph]
[23]	Proctor T, Rudingfer K, Young K, Sarovar M and Blume-Kohout R 2017 Phys. Rev. Lett. 119 130502 doi: 10.1103/PhysRevLett.119.130502
[24]	Dankert C, Cleve R, Emerson J and Livine E 2006 Phys. Rev. A 80 012304
[25]	Roy A and Scott A J 2009 Designs Codes and Cryptography 53 13 doi: 10.1007/s10623-009-9290-2
[26]	Ambainis A, Mosca M, Tapp A and De Wolf D 2000 41st Annual Symposium on Foundations of Computer Science, 2000, Redondo Beach, California, p. 547
[27]	Radhakrishnan J, Röetteler M and Sen P 2009 Algorithmica 55 490 doi: 10.1007/s00453-008-9231-x
[28]	Ambainis A and Emerson J 2007 22nd Annual IEEE Conference on Computational Complexity, June, 13-16, 2007, San Diego, California, p. 129)
[29]	Brown W G and Viola L 2009 Phys. Rev. Lett. 104 250501
[30]	Bannai E and Bannai E 2009 European Journal of Combinatorics 30 1392 doi: 10.1016/j.ejc.2008.11.007
[31]	Delsarte P, Goethals J M and Seidel J J 1991 Geometriae Dedicata 6 68
[32]	Benedetto J J and Fickus M 2003 Advances in Computational Mathematics 18 357 doi: 10.1023/A:1021323312367
[33]	Gross D, Audenaert K and Eisert J 2007 Journal of Mathematical Physics 48 052104 doi: 10.1063/1.2716992
[34]	Emerson J, Alicki R and Zyczkowski K 2005 J. Opt. B: Quantum Semiclass. Opt. 7 347 doi: 10.1088/1464-4266/7/10/021
[35]	Goodman R and Wallach N R 2009 Symmetry, Representations, and Invariants (New York: Springer) pp. 180-181
[36]	Hoeffding W 1963 J. Am. Statistical Assoc 58 13 doi: 10.1080/01621459.1963.10500830
[37]	Sanders Y R, Wallman J J and Sanders B C 2016 New J. Phys. 18 012002

Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design

Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design

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