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利用非稳定子态容错实现密集旋转操作

吴向艳 徐艳玲 於亚飞 张智明

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利用非稳定子态容错实现密集旋转操作

吴向艳, 徐艳玲, 於亚飞, 张智明

Fault-tolerantly implementing dense rotation operations based on non-stabilizer states

Wu Xiang-Yan, Xu Yan-Ling, Yu Ya-Fei, Zhang Zhi-Ming
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  • Non-Clifford操作不能在量子纠错码上自然横向实现, 但可通过辅助量子态和在量子纠错码上能横向实现的Clifford操作来容错实现, 从而取得容错量子计算的通用性. 非平庸的单量子比特操作是Non-Clifford操作, 可以分解为绕z轴和绕x轴非平庸旋转操作的组合. 本文首先介绍了利用非稳定子态容错实现绕z轴和绕x轴旋转的操作, 进而设计线路利用魔幻态容错制备非稳定子态集, 最后讨论了运用制备的非稳定子态集模拟任意非平庸单量子比特操作的问题. 与之前工作相比, 制备非稳定子态的线路得到简化, 成功概率提高, 且在高精度模拟任意单量子比特操作时所消耗的非稳定子态数目减少了50%.
    Based on the quantum error-correction codes and concatenation, quantum logical gates can be implemented transversally, which is called the fault-tolerant quantum computation. Clifford gates can be directly and fault-tolerantly performed, but they cannot reach universal quantum computation. How to implement the non-Clifford gate fault-tolerantly is a vital technique in fault-tolerant universal quantum computation. Here the magic state is selected to help the implementing of the non-Clifford gate transversally. Based on the non-stabilizer state cos θi|0>+sinθi|1>, circuits which can execute 2θi rotation around X-axis and Z-axis fault-tolerantly are proposed. Then new non-stabilizer states in this form are developed and produced from the distilled magic state. By using these states, a number of non-Clifford gates can be performed transversally, which makes profound implication in fault-tolerant quantum computation. We calculate the number of the non-stabilizer states needed for simulating the desired rotation operations, which is less than that in previous protocols.
    • 基金项目: 国家自然科学基金(批准号:61378012,60978009)、高等学校博士学科点专项科研基金(批准号:20124407110009)、国家重点基础研究发展计划(批准号:2011CBA00200,2013CB921804)和国家教育部留学回国人员科研启动基金资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61378012, 60978009), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20124407110009), the National Basic Research Program of China (Grant Nos. 2011CBA00200, 2013CB921804) and Scientific Research Staring Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China.
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    Sun J, Lu S F, Liu F, Yang L P 2012 Chin. Phys. B 21 010306

    [2]

    Chen W, Xue Z Y, Wang Z D, Shen R 2014 Chin. Phys. B 23 030309

    [3]

    Li T, Bao W S, Lin W Q, Zhang H, Fu X Q 2014 Chin. Phys. Lett. 31 050301

    [4]

    Li H Y, Wu C W, Chen Y B, Lin Y G, Chen P X, Li C Z 2013 Chin. Phys. B 22 110305

    [5]

    Wang X X, Zhang J Q, Yu Y F, Zhang Z M 2011 Chin. Phys. B 20 110306

    [6]

    Bacon D, Kempe J, Lidar D A, Whaley K B 2000 Phys. Rev. Lett. 85 1758

    [7]

    Zhang Q, Zhang E Y, Tang C J 2002 Acta Phys. Sin. 51 1675 (in Chinese) [张权, 张尔扬, 唐朝京 2002 物理学报 51 1675]

    [8]

    Raussendorf R, Harrington J, Goyal K 2007 New J. Phys. 9 199

    [9]

    Gottesman D 1997 Ph. D. Dissertation (California: Caltech)

    [10]

    Li Z, Xing L J 2013 Acta Phys. Sin. 62 130306 (in Chinese) [李卓, 刑莉娟 2013 物理学报 62 130306]

    [11]

    Xiao F Y, Chen H W 2010 Acta Phys. Sin. 60 080303 (in Chinese) [肖芳英, 陈汉武 2010 物理学报 60 080303]

    [12]

    Nielsen M A , Chuang I L 2000 Quantum Computation and Quantum Information (Vol.1) (Cambridge, England: Cambridge University Press) p179

    [13]

    Eastin B 2013 Phys. Rev. A 87 032321

    [14]

    Landahl A J, Cesare C 2013 Preprint arXiv: 1302.3240

    [15]

    Jochym-O'connor T, Laflamme R 2014 Phys. Rev. Lett. 112 010505

    [16]

    Paetznick A, Reichardt B W 2013 Phys. Rev. Lett. 111 090505

    [17]

    Bravyi S, Kitaev A 2005 Phys. Rev. A 71 022316

    [18]

    Duclos-Cianci G, Svore K M 2013 Phys. Rev. A 88 042325

    [19]

    Howard M, Wallman J, Veitch V, Emerson J 2014 Nature 510 351

    [20]

    Jochym-O'connor T, Yu Y, Helou B, Laflamme R 2013 Quantum Inf. Comput. 13 361

    [21]

    Yu Y F, Zhang Z M 2013 Acta Sin. Quantum Opt. 19 330 (in Chinese) [於亚飞, 张智明 2013 量子光学学报 19 330]

    [22]

    Reichardt B W 2005 Quantum Inf. Process 4 251

    [23]

    Campbell E T, Anwar H, Browne D E 2012 Phys. Rev. X 2 041021

    [24]

    Bravyi S, Haah J 2012 Phys. Rev. A 86 052329

    [25]

    Anwar H, Campbell E T, Browne D E 2012 New J. Phys. 14 063006

    [26]

    Meier A M, Eastin B, Knill E 2013 Quantum Inf. Comput. 13 195

    [27]

    Reichardt B W 2009 Quantum Inf. Comput. 9 1030

    [28]

    Jones C 2013 Phys. Rev. A 87 042305

    [29]

    Campbell E T, Browne D E 2010 Phys. Rev. Lett. 104 030503

    [30]

    Jones N C, Van M R, Fowler A G, McMahon P L, Kim J, Ladd T D, Yamamoto Y 2012 Phys. Rev. X 2 031007

    [31]

    Fowler A G, Mariantoni M, Martinis J M, Cleland A N 2012 Phys. Rev. A 86 032324

    [32]

    Sun J G, He Y G 2003 J. Software 14 334 (in Chinese) [孙吉贵, 何雨果 2003 软件学报 14 334]

    [33]

    Grover L K 1996 Proc. 28th ACM Symp. Theory of Comp. May 22-24, 1996, p212-219

    [34]

    Bocharov A, Svore K M 2012 Phys. Rev. Lett. 109 190501

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出版历程
  • 收稿日期:  2014-06-23
  • 修回日期:  2014-09-08
  • 刊出日期:  2014-11-05

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