Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design
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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 unitary2t-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).
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 unitary2t-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).
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 unitary2t-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).
引文
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[19]Wallman J J and Flammia S T 2014 New J.Phys.16 103032
[20]Wallman J J,Barnhill M,Emerson J 2016 New J.Phys.18 043021
[21]Wallman J J and Emerson J 2016 Phys.Rev.A 94 052325
[22]Helsen J,Wallman J J,Flammia S T and Wehner S 2017arXiv:1701.04299v1[quant-ph]
[23]Proctor T,Rudingfer K,Young K,Sarovar M and Blume-Kohout R2017 Phys.Rev.Lett.119 130502
[24]Dankert C,Cleve R,Emerson J and Livine E 2006 Phys.Rev.A 80012304
[25]Roy A and Scott A J 2009 Designs Codes and Cryptography 53 13
[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,Roetteler M and Sen P 2009 Algorithmica 55 490
[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 301392
[31]Delsarte P,Goethals J M and Seidel J J 1991 Geometriae Dedicata 668
[32]Benedetto J J and Fickus M 2003 Advances in Computational Mathematics 18 357
[33]Gross D,Audenaert K and Eisert J 2007 Journal of Mathematical Physics 48 052104
[34]Emerson J,Alicki R and Zyczkowski K 2005 J.Opt.B:Quantum Semiclass.Opt.7 347
[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
[37]Sanders Y R,Wallman J J and Sanders B C 2016 New J.Phys.18012002
[2]Aliferis P,Gottesman D and Preskill J 2005 Quantum Info.Comput.697
[3]Kueng R,Long D M,Doherty A C and Flammia S T 2016 Phys.Rev.Lett.117 170502
[4]D’Ariano G M,Paris M G A and Sacchi M F 2003 Advances in Imaging and Electron Physics 128 205
[5]Artiles L M,Gill R D and Guta M I Journal of Royal Statistical Society2004 Journal of Royal Statistical Society 67 109
[6]Poyatos J F,Cirac J I and Zoller P 1997 Phys.Rev.Lett.78 390
[7]Wei S J,Xin T and Long G L 2018 Sci.China-Phys.Mech.Astron.61070311
[8]Horodecki M,Horodecki P and Horodecki R 1998 Phys.Rev.A 601888
[9]Xu Y Y,Zhou F,Chen L,Xie Y,Xue P and Feng M 2012 Chin.Phys.B 21 040304
[10]Wu W,Liu X and Wang C 2018 Chin.Phys.B 27 060302
[11]Chen N,Quan D X,Xu F F,Yang H and Pei C X 2015 Chin.Phys.B24 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
[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.106180504
[16]Gaebler J P,Meier A M,Tan T R,Bowler R,Lin Y,Hanneke D,Jost JD,Home J P,Knill E,Leibfried D and Wineland D J 2012 Phys.Rev.Lett.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
[18]Magesan E,Gambetta J M,Emerson J 2012 Phys.Rev.A 85 042311
[19]Wallman J J and Flammia S T 2014 New J.Phys.16 103032
[20]Wallman J J,Barnhill M,Emerson J 2016 New J.Phys.18 043021
[21]Wallman J J and Emerson J 2016 Phys.Rev.A 94 052325
[22]Helsen J,Wallman J J,Flammia S T and Wehner S 2017arXiv:1701.04299v1[quant-ph]
[23]Proctor T,Rudingfer K,Young K,Sarovar M and Blume-Kohout R2017 Phys.Rev.Lett.119 130502
[24]Dankert C,Cleve R,Emerson J and Livine E 2006 Phys.Rev.A 80012304
[25]Roy A and Scott A J 2009 Designs Codes and Cryptography 53 13
[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,Roetteler M and Sen P 2009 Algorithmica 55 490
[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 301392
[31]Delsarte P,Goethals J M and Seidel J J 1991 Geometriae Dedicata 668
[32]Benedetto J J and Fickus M 2003 Advances in Computational Mathematics 18 357
[33]Gross D,Audenaert K and Eisert J 2007 Journal of Mathematical Physics 48 052104
[34]Emerson J,Alicki R and Zyczkowski K 2005 J.Opt.B:Quantum Semiclass.Opt.7 347
[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
[37]Sanders Y R,Wallman J J and Sanders B C 2016 New J.Phys.18012002