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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 64 , Issue 5 : 250362(2021) https://doi.org/10.1007/s11433-020-1641-1

Experimental realization of nonadiabatic geometric gates with a superconducting Xmon qubit

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  • ReceivedOct 16, 2020
  • AcceptedNov 17, 2020
  • PublishedFeb 9, 2021
PACS numbers

Abstract


Acknowledgment

This work was supported by the National Basic Research Program of China (Grant No. 2015CB921004), the National Key Research and Development Program of China (Grant Nos. 2019YFA0308602, and 2016YFA0301700), the National Natural Science Foundation of China (Grant Nos. 11934010, and 11775129), the Fundamental Research Funds for the Central Universities in China, and the Anhui Initiative in Quantum Information Technologies (Grant No. AHY080000). Yi Yin acknowledge the funding support from Tencent Corporation. This work was partially conducted at the Center for Micro- and Nanoscale Research and Fabrication, University of Science and Technology of China.


References

[1] Bremner M. J., Dawson C. M., Dodd J. L., Gilchrist A., Harrow A. W., Mortimer D., Nielsen M. A., Osborne T. J.. Phys. Rev. Lett., 2002, 89: 247902 CrossRef PubMed ADS arXiv Google Scholar

[2] De Chiara G., Palma G. M.. Phys. Rev. Lett., 2003, 91: 090404 CrossRef PubMed ADS arXiv Google Scholar

[3] Carollo A., Fuentes-Guridi I., Santos M. F., Vedral V.. Phys. Rev. Lett., 2004, 92: 020402 CrossRef PubMed ADS arXiv Google Scholar

[4] Solinas P., Zanardi P., Zanghì N.. Phys. Rev. A, 2004, 70: 042316 CrossRef ADS arXiv Google Scholar

[5] Zhu S. L., Zanardi P.. Phys. Rev. A, 2005, 72: 020301(R) CrossRef ADS arXiv Google Scholar

[6] Thomas J. T., Lababidi M., Tian M.. Phys. Rev. A, 2011, 84: 042335 CrossRef ADS Google Scholar

[7] Johansson M., Sj?qvist E., Andersson L. M., Ericsson M., Hessmo B., Singh K., Tong D. M.. Phys. Rev. A, 2012, 86: 062322 CrossRef ADS arXiv Google Scholar

[8] Zanardi P., Rasetti M.. Phys. Lett. A, 1999, 264: 94-99 CrossRef Google Scholar

[9] Jones J. A., Vedral V., Ekert A., Castagnoli G.. Nature, 2000, 403: 869-871 CrossRef PubMed ADS arXiv Google Scholar

[10] Duan L. M.. Science, 2001, 292: 1695-1697 CrossRef PubMed ADS arXiv Google Scholar

[11] Proc. R. Soc. Lond. A, 1984, 392: 45-57 CrossRef ADS

[12] Wilczek F., Zee A.. Phys. Rev. Lett., 1984, 52: 2111-2114 CrossRef ADS Google Scholar

[13] Xiang-Bin W., Keiji M.. Phys. Rev. Lett., 2001, 87: 097901 CrossRef PubMed ADS arXiv Google Scholar

[14] Zhu S. L., Wang Z. D.. Phys. Rev. Lett., 2002, 89: 097902 CrossRef PubMed ADS arXiv Google Scholar

[15] Aharonov Y., Anandan J.. Phys. Rev. Lett., 1987, 58: 1593-1596 CrossRef PubMed ADS Google Scholar

[16] Sj?qvist E., Tong D. M., Mauritz Andersson L., Hessmo B., Johansson M., Singh K.. New J. Phys., 2012, 14: 103035 CrossRef ADS arXiv Google Scholar

[17] Xu G. F., Zhang J., Tong D. M., Sj?qvist E., Kwek L. C.. Phys. Rev. Lett., 2012, 109: 170501 CrossRef PubMed ADS arXiv Google Scholar

[18] Anandan J.. Phys. Lett. A, 1988, 133: 171-175 CrossRef Google Scholar

[19] Zhu S. L., Wang Z. D.. Phys. Rev. Lett., 2003, 91: 187902 CrossRef PubMed ADS arXiv Google Scholar

[20] Feng X. L., Wu C., Sun H., Oh C. H.. Phys. Rev. Lett., 2009, 103: 200501 CrossRef PubMed ADS Google Scholar

[21] Ota Y., Kondo Y.. Phys. Rev. A, 2009, 80: 024302 CrossRef ADS arXiv Google Scholar

[22] Spiegelberg J., Sj?qvist E.. Phys. Rev. A, 2013, 88: 054301 CrossRef ADS arXiv Google Scholar

[23] Xu G., Long G.. Phys. Rev. A, 2014, 90: 022323 CrossRef ADS Google Scholar

[24] Liang Z. T., Du Y. X., Huang W., Xue Z. Y., Yan H.. Phys. Rev. A, 2014, 89: 062312 CrossRef ADS Google Scholar

[25] Xue Z. Y., Zhou J., Wang Z. D.. Phys. Rev. A, 2015, 92: 022320 CrossRef ADS arXiv Google Scholar

[26] Xu G. F., Liu C. L., Zhao P. Z., Tong D. M.. Phys. Rev. A, 2015, 92: 052302 CrossRef ADS arXiv Google Scholar

[27] Sj?qvist E.. Phys. Lett. A, 2016, 380: 65-67 CrossRef ADS arXiv Google Scholar

[28] Albert V. V., Shu C., Krastanov S., Shen C., Liu R. B., Yang Z. B., Schoelkopf R. J., Mirrahimi M., Devoret M. H., Jiang L.. Phys. Rev. Lett., 2016, 116: 140502 CrossRef PubMed ADS arXiv Google Scholar

[29] Zhao P. Z., Xu G. F., Tong D. M.. Phys. Rev. A, 2016, 94: 062327 CrossRef ADS arXiv Google Scholar

[30] Herterich E., Sj?qvist E.. Phys. Rev. A, 2016, 94: 052310 CrossRef ADS arXiv Google Scholar

[31] Zhao P. Z., Xu G. F., Ding Q. M., Sj?qvist E., Tong D. M.. Phys. Rev. A, 2017, 95: 062310 CrossRef ADS arXiv Google Scholar

[32] Zhao P. Z., Cui X. D., Xu G. F., Sj?qvist E., Tong D. M.. Phys. Rev. A, 2017, 96: 052316 CrossRef ADS arXiv Google Scholar

[33] Chen T., Xue Z. Y.. Phys. Rev. Appl., 2018, 10: 054051 CrossRef ADS arXiv Google Scholar

[34] Zhao P. Z., Wu X., Xing T. H., Xu G. F., Tong D. M.. Phys. Rev. A, 2018, 98: 032313 CrossRef ADS arXiv Google Scholar

[35] Zhao P. Z., Xu G. F., Tong D. M.. Phys. Rev. A, 2019, 99: 052309 CrossRef ADS arXiv Google Scholar

[36] Leibfried D., DeMarco B., Meyer V., Lucas D., Barrett M., Britton J., Itano W. M., Jelenkovi? B., Langer C., Rosenband T., Wineland D. J.. Nature, 2003, 422: 412-415 CrossRef PubMed ADS Google Scholar

[37] Du J., Zou P., Wang Z. D.. Phys. Rev. A, 2006, 74: 020302(R) CrossRef ADS arXiv Google Scholar

[38] Feng G., Xu G., Long G.. Phys. Rev. Lett., 2013, 110: 190501 CrossRef PubMed ADS arXiv Google Scholar

[39] Li H., Liu Y., Long G. L.. Sci. China-Phys. Mech. Astron., 2017, 60: 080311 CrossRef ADS arXiv Google Scholar

[40] Abdumalikov Jr A. A., Fink J. M., Juliusson K., Pechal M., Berger S., Wallraff A., Filipp S.. Nature, 2013, 496: 482-485 CrossRef PubMed ADS arXiv Google Scholar

[41] Xu Y., Cai W., Ma Y., Mu X., Hu L., Chen T., Wang H., Song Y. P., Xue Z. Y., Yin Z., Sun L.. Phys. Rev. Lett., 2018, 121: 110501 CrossRef PubMed ADS arXiv Google Scholar

[42] Zhang Z., Zhao P. Z., Wang T., Xiang L., Jia Z., Duan P., Tong D. M., Yin Y., Guo G.. New J. Phys., 2019, 21: 073024 CrossRef ADS arXiv Google Scholar

[43] Danilin S., Veps?l?inen A., Paraoanu G. S.. Phys. Scr., 2018, 93: 055101 CrossRef ADS arXiv Google Scholar

[44] Egger D. J., Ganzhorn M., Salis G., Fuhrer A., Müller P., Barkoutsos P. K., Moll N., Tavernelli I., Filipp S.. Phys. Rev. Appl., 2019, 11: 014017 CrossRef ADS arXiv Google Scholar

[45] Zu C., Wang W. B., He L., Zhang W. G., Dai C. Y., Wang F., Duan L. M.. Nature, 2014, 514: 72-75 CrossRef PubMed ADS arXiv Google Scholar

[46] Arroyo-Camejo S., Lazariev A., Hell S. W., Balasubramanian G.. Nat. Commun., 2014, 5: 4870 CrossRef PubMed ADS Google Scholar

[47] Zhou B. B., Jerger P. C., Shkolnikov V. O., Heremans F. J., Burkard G., Awschalom D. D.. Phys. Rev. Lett., 2017, 119: 140503 CrossRef PubMed ADS arXiv Google Scholar

[48] Sekiguchi Y., Niikura N., Kuroiwa R., Kano H., Kosaka H.. Nat. Photon, 2017, 11: 309-314 CrossRef ADS arXiv Google Scholar

[49] Nagata K., Kuramitani K., Sekiguchi Y., Kosaka H.. Nat. Commun., 2018, 9: 3227 CrossRef PubMed ADS Google Scholar

[50] Ishida N., Nakamura T., Tanaka T., Mishima S., Kano H., Kuroiwa R., Sekiguchi Y., Kosaka H.. Opt. Lett., 2018, 43: 2380 CrossRef PubMed ADS Google Scholar

[51] Zhang F., Zhang J., Gao P., Long G.. Phys. Rev. A, 2019, 100: 012329 CrossRef ADS Google Scholar

[52] J. Zhang, T. H. Kyaw, D. M. Tong, E. Sjöqvist, and L. C. Kwek, Sci. Rep. 5, 18414 (2015). Google Scholar

[53] Liang Z. T., Yue X., Lv Q., Du Y. X., Huang W., Yan H., Zhu S. L.. Phys. Rev. A, 2016, 93: 040305(R) CrossRef ADS arXiv Google Scholar

[54] Berry M. V.. J. Phys. A-Math. Theor., 2009, 42: 365303 CrossRef ADS Google Scholar

[55] Klei?ler F., Lazariev A., Arroyo-Camejo S.. npj Quantum Inf, 2018, 4: 49 CrossRef ADS arXiv Google Scholar

[56] Yan T., Liu B. J., Xu K., Song C., Liu S., Zhang Z., Deng H., Yan Z., Rong H., Huang K., Yung M. H., Chen Y., Yu D.. Phys. Rev. Lett., 2019, 122: 080501 CrossRef PubMed ADS arXiv Google Scholar

[57] Wang T., Zhang Z., Xiang L., Jia Z., Duan P., Cai W., Gong Z., Zong Z., Wu M., Wu J., Sun L., Yin Y., Guo G.. New J. Phys., 2018, 20: 065003 CrossRef ADS arXiv Google Scholar

[58] Veps?l?inen A., Danilin S., Paraoanu G. S.. Sci. Adv., 2019, 5: eaau5999 CrossRef PubMed ADS arXiv Google Scholar

[59] Veps?l?inen A., Danilin S., Paraoanu G. S.. Quantum Sci. Technol., 2018, 3: 024006 CrossRef ADS arXiv Google Scholar

[60] Koch J., Yu T. M., Gambetta J., Houck A. A., Schuster D. I., Majer J., Blais A., Devoret M. H., Girvin S. M., Schoelkopf R. J.. Phys. Rev. A, 2007, 76: 042319 CrossRef ADS Google Scholar

[61] Barends R., Kelly J., Megrant A., Sank D., Jeffrey E., Chen Y., Yin Y., Chiaro B., Mutus J., Neill C., O'Malley P., Roushan P., Wenner J., White T. C., Cleland A. N., Martinis J. M.. Phys. Rev. Lett., 2013, 111: 080502 CrossRef PubMed ADS arXiv Google Scholar

[62] Barends R., Kelly J., Megrant A., Veitia A., Sank D., Jeffrey E., White T. C., Mutus J., Fowler A. G., Campbell B., Chen Y., Chen Z., Chiaro B., Dunsworth A., Neill C., O'Malley P., Roushan P., Vainsencher A., Wenner J., Korotkov A. N., Cleland A. N., Martinis J. M.. Nature, 2014, 508: 500-503 CrossRef PubMed ADS arXiv Google Scholar

[63] Kelly J., Barends R., Fowler A. G., Megrant A., Jeffrey E., White T. C., Sank D., Mutus J. Y., Campbell B., Chen Y., Chen Z., Chiaro B., Dunsworth A., Hoi I. C., Neill C., O'Malley P. J. J., Quintana C., Roushan P., Vainsencher A., Wenner J., Cleland A. N., Martinis J. M.. Nature, 2015, 519: 66-69 CrossRef PubMed Google Scholar

[64] Chow J. M., Gambetta J. M., Tornberg L., Koch J., Bishop L. S., Houck A. A., Johnson B. R., Frunzio L., Girvin S. M., Schoelkopf R. J.. Phys. Rev. Lett., 2009, 102: 090502 CrossRef PubMed ADS arXiv Google Scholar

[65] Magesan E., Gambetta J. M., Emerson J.. Phys. Rev. Lett., 2011, 106: 180504 CrossRef PubMed ADS arXiv Google Scholar

[66] Magesan E., Gambetta J. M., Johnson B. R., Ryan C. A., Chow J. M., Merkel S. T., da Silva M. P., Keefe G. A., Rothwell M. B., Ohki T. A., Ketchen M. B., Steffen M.. Phys. Rev. Lett., 2012, 109: 080505 CrossRef PubMed ADS arXiv Google Scholar

[67] Wang X., Sun Z., Wang Z. D.. Phys. Rev. A, 2009, 79: 012105 CrossRef ADS arXiv Google Scholar

[68] Xu Y., Hua Z., Chen T., Pan X., Li X., Han J., Cai W., Ma Y., Wang H., Song Y. P., Xue Z. Y., Sun L.. Phys. Rev. Lett., 2020, 124: 230503 CrossRef PubMed ADS arXiv Google Scholar

  • Figure 1

    (Color online) Schematic setup for the realization of nonadiabatic geometric gates. (a) The evolution path of state $|\psi_{+}\rangle$ with Bloch sphere representation. The state $|\psi_{+}\rangle$ is driven by the designed microwave pulses along an orange slice-shaped path in the computational space and acquires a geometric phase $-\gamma/2$. (b) The cross-shaped architecture of superconducting Xmon.

  • Figure 2

    (Color online) Quantum process tomography for nonadiabatic geometric gates. (a) The schematic diagram for the quantum process tomography; (b) the matrix elements generated by Hadamard gate $H$ with the real part on the left and the imaginary part on the right, where $\chi$ is the process matrix; (c) the process fidelities of nonadiabatic geometric gates.

  • Figure 3

    (Color online) Clifford-based randomized benchmarking of nonadiabatic geometric gates. The inset describes the process of reference and interleaved randomized benchmarking. Sequence fidelities are displayed as functions of the number of Cliffords, where each sequence is averaged over $50$ randomized operations.

  • Figure 4

    (Color online) Noise-resilient feature of geometric gates. (a)-(c) The experimental and numerical fidelities of quantum gates as functions of the pulse amplitude error under geometric manipulation and dynamical manipulation; (d)-(f) the experimental and numerical fidelities of quantum gates as functions of the frequency shift-induced error under geometric manipulation and dynamical manipulation.

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