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基于冗余图态的多人协作量子计算

田宇玲 冯田峰 周晓祺

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基于冗余图态的多人协作量子计算

田宇玲, 冯田峰, 周晓祺

Collaborative quantum computation with redundant graph state

Tian Yu-Ling, Feng Tian-Feng, Zhou Xiao-Qi
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  • 量子计算是一种基于量子力学基本原理设计的新型计算模型, 在某些特定问题上表现出了远超经典计算机的处理能力. 随着量子计算任务复杂度的提高, 如何分配量子计算资源, 实现多方协作的量子计算, 将成为量子计算领域待解决的一个重要问题. 本文在一次性量子计算的基础上, 提出了基于冗余图态的多人协作量子计算方案. 不同于传统图态中每个节点仅对应一个粒子, 冗余图态中每个节点都对应若干粒子. 参与量子计算的每一方都将分配到一组完整涵盖各节点的粒子, 各方将自行协商完成图态的分割以及后续的测量, 从而实现多人协作的量子计算. 在本方案中, 参与量子计算的各方可以根据自身任务的需要来确定量子计算的合作方式并进行资源分配, 使量子计算具备更高的灵活性与开放性. 此外, 本文还提出了一个两方协作制备任意单比特量子态的光学实验方案.
    Quantum computation is a computing model based on quantum theory, which can outperform the classical computation in solving certain problems. With the increase of the complexity of quantum computing tasks, it becomes important to distribute quantum computing resources to multi-parties to cooperatively fulfill the complex tasks. Here in this paper a scheme based on the one-way quantum computing model is proposed to realize collaborative quantum computation. The standard one-way quantum computing model is based on graph states. With graph states used as resources, one can realize a universal quantum computer through using single-qubit measurements and feed-forward. In contrast to the standard one-way computation, the main resource for collaborative quantum computation is a redundant graph state (also a multi-particle highly entangled state). Unlike in the traditional graph state where each particle corresponds to a specific node, in a redundant graph state, several particles correspond to a single node, which means that each node of the graph has several redundant copies. With the help of a redundant graph state, several parties can share a graph state flexibly at will. A redundant graph state is prepared and then distributed to several parties where each of them obtains a full copy of all nodes. By communicating with each other and measuring the particles in different ways, a standard graph state is prepared and distributed among these parties. The collaborative computation then finishes through the common one-way quantum computing operations. Besides the general scheme, a concrete optical implementation of a two-party cooperative single-qubit quantum state preparation based on a six-photon redundant graph state is also put forward. Such a redundant graph state is proposed to be prepared by using the spontaneous parametric down-conversion entangled source and quantum interference. With this redundant graph state, a standard three-node graph state can be shared with the two parties in an arbitrary way. This scheme does not only make the collaborative quantum computation across several parties possible and flexible, but also guarantee the privacy of each party’s operations. This feature would be particularly useful in the case where the computing resource is obtained from an outside provider. This scheme paves the way for realizing quantum computation in more general and complicated applications.
      通信作者: 周晓祺, zhouxq8@mail.sysu.edu.cn
    • 基金项目: 国家重点研发计划(批准号: 2017YFA0305200, 2016YFA0301700)和广东省自然科学基金(批准号: 2016A030312012)资助的课题.
      Corresponding author: Zhou Xiao-Qi, zhouxq8@mail.sysu.edu.cn
    • Funds: Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0305200, 2016YFA0301700) and the Natural Science Foundation of Guangdong Province, China (Grant No. 2016A030312012).
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    Benioff P 1980 J. Stat. Phys. 22 563Google Scholar

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    Deutsch D 1985 Proc. R. Soc. Lond. A 400 97Google Scholar

    [4]

    Shor P W 1994 Proceedings 35th Annual Symposium on Foundations of Computer Science Santa Fe, NM, USA, Nov. 20-22, 1994 p124

    [5]

    Grover L K 1997 Phys. Rev. Lett. 79 325Google Scholar

    [6]

    Aspuru-Guzik A, Dutoi A D, Love P J, Head-Gordon M 2005 Science 309 1704Google Scholar

    [7]

    Jordan S P, Lee K S M, Preskill J 2012 Science 336 1130Google Scholar

    [8]

    O’Malley P J J, Babbush R, Kivlichan I D, et al. 2016 Phys. Rev. X 6 031007

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    Cai X D, Weedbrook C, Su Z E, Chen M C, Gu M, Zhu M J, Li L, Liu N L, Lu C Y, Pan J W 2013 Phys. Rev. Lett. 110 230501Google Scholar

    [10]

    Li Z K, Liu X M, Xu N Y, Du J F 2015 Phys. Rev. Lett. 114 140504Google Scholar

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    Wang H, He Y, Li Y H, Su Z E, Li B, Huang H L, Ding X, Chen M C, Liu C, Qin J, Li J P, He Y M, Schneider C, Kamp M, Peng C Z, Höfling S, Lu C Y, Pan J W 2017 Nat. Photon. 11 361Google Scholar

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    Qiang X G, Zhou X Q, Wang J W, Wilkes C M, Loke T, O’Gara S, Kling L, Marshall G D, Santagati R, Ralph T C, Wang J B, O’Brien J L, Thompson M G, Matthews J C F 2018 Nat. Photon. 12 534Google Scholar

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    Deutsch D E 1989 Proc. R. Soc. Lond. A 425 73Google Scholar

    [14]

    Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188Google Scholar

    [15]

    Walther P, Resch K J, Rudolph T, Schenck E, Weinfurter H, Vedral V, Aspelmeyer M, Zeilinger A 2005 Nature 434 169Google Scholar

    [16]

    Chen X, Gu Z C, Wen X G 2010 Phys. Rev. B 82 155138Google Scholar

    [17]

    Luo Z H, Li J, Li Z K, Hung L Y, Wan Y D, Peng X H, Du J F 2018 Nat. Phys. 14 160Google Scholar

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    Farhi E, Goldstone J, Gutmann S, Sipser M 2000 arXiv: 0001106v1 [quant-ph]

    [19]

    Long G L 2006 Commun. Math. Phys. 45 825

    [20]

    Ladd T D, Jelezko F, Laflamme R, Nakamura Y, Monroe C, O’Brien J L 2010 Nature 464 45Google Scholar

    [21]

    周晓祺 2008 博士学位论文 (合肥: 中国科学技术大学)

    Zhou X Q 2008 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)

    [22]

    Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910Google Scholar

    [23]

    Raussendorf R, Browne D E, Briegel H J 2003 Phys. Rev. A 68 022312Google Scholar

    [24]

    Bouchet A 1993 Discrete Math. 114 75Google Scholar

    [25]

    Fujii K 2015 arXiv: 1504.01444v1 [quant-ph]

    [26]

    Varnava M, Browne D E, Rudolph T 2006 Phys. Rev. Lett. 97 120501Google Scholar

    [27]

    Zhao Z, Chen Y A, Zhang A N, Yang T, Briegel H J, Pan J W 2004 Nature 430 54Google Scholar

  • 图 1  对图态进行局域泡利测量并进行相应的幺正变换后得到新图态 (a)对图态中的任何一个粒子进行σz测量; (b)对图态上相邻的两个粒子分别进行σx测量; (c)对粒子5a, 5b进行σx测量, 对n个粒子5c中的任意一个粒子5ci进行M测量, 其余的n – 1个粒子进行σz测量; (d)对粒子5做一个单比特测量M

    Fig. 1.  Graph states after local measurements and the corresponding unitary operations: (a) σz measurement on any particle in the graph state; (b) two neighboring σx measurements on the graph state; (c) σx measurements on 5a, 5b, measurement M on 5ci and σz measurements on 5ck(ki); (d) measurement M on single-qubit 5.

    图 2  基于冗余图态的多人协作量子计算 (a) 用于两人协作量子计算的图态; (b) “工”字形冗余图态; (c) 对(b)图所示图态中的b1, b2, b3, a4, a5, a6进行σz测量后剩下的图态; (d) 对(b)图所示图态中的a1, a2, a3, b4, b5, b6进行σz测量后剩下的图态; (e)用于多人协作量子计算的图态

    Fig. 2.  Collaborative computation based on redundant graph state: (a) A graph state for bipartite collaborative quantum computation; (b) an I-shape redundant graph state; (c) the graph state after σz measurements on b1, b2, b3, a4, a5, a6 in graph state depicted in (b); (d) the graph state after σz measurements on a1, a2, a3, b4, b5, b6 in graph state depicted in (b); (e) a graph state for collaborative quantum computation.

    图 3  冗余图态 (a)任意的冗余图态; (b)与图(a)相对应的传统图态; (c)六粒子冗余图态

    Fig. 3.  Redundant graph state: (a) An arbitrary redundant graph state; (b) the traditional graph state corresponding to (a); (c) six-partite redundant graph state.

    图 4  两用户协作制备任意单比特量子态的光学实验装置

    Fig. 4.  Physical realization of preparing arbitrary quantum state cooperated by two participants in optics.

  • [1]

    Feynman R P 1982 Int. J. Theor. Phys. 21 467Google Scholar

    [2]

    Benioff P 1980 J. Stat. Phys. 22 563Google Scholar

    [3]

    Deutsch D 1985 Proc. R. Soc. Lond. A 400 97Google Scholar

    [4]

    Shor P W 1994 Proceedings 35th Annual Symposium on Foundations of Computer Science Santa Fe, NM, USA, Nov. 20-22, 1994 p124

    [5]

    Grover L K 1997 Phys. Rev. Lett. 79 325Google Scholar

    [6]

    Aspuru-Guzik A, Dutoi A D, Love P J, Head-Gordon M 2005 Science 309 1704Google Scholar

    [7]

    Jordan S P, Lee K S M, Preskill J 2012 Science 336 1130Google Scholar

    [8]

    O’Malley P J J, Babbush R, Kivlichan I D, et al. 2016 Phys. Rev. X 6 031007

    [9]

    Cai X D, Weedbrook C, Su Z E, Chen M C, Gu M, Zhu M J, Li L, Liu N L, Lu C Y, Pan J W 2013 Phys. Rev. Lett. 110 230501Google Scholar

    [10]

    Li Z K, Liu X M, Xu N Y, Du J F 2015 Phys. Rev. Lett. 114 140504Google Scholar

    [11]

    Wang H, He Y, Li Y H, Su Z E, Li B, Huang H L, Ding X, Chen M C, Liu C, Qin J, Li J P, He Y M, Schneider C, Kamp M, Peng C Z, Höfling S, Lu C Y, Pan J W 2017 Nat. Photon. 11 361Google Scholar

    [12]

    Qiang X G, Zhou X Q, Wang J W, Wilkes C M, Loke T, O’Gara S, Kling L, Marshall G D, Santagati R, Ralph T C, Wang J B, O’Brien J L, Thompson M G, Matthews J C F 2018 Nat. Photon. 12 534Google Scholar

    [13]

    Deutsch D E 1989 Proc. R. Soc. Lond. A 425 73Google Scholar

    [14]

    Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188Google Scholar

    [15]

    Walther P, Resch K J, Rudolph T, Schenck E, Weinfurter H, Vedral V, Aspelmeyer M, Zeilinger A 2005 Nature 434 169Google Scholar

    [16]

    Chen X, Gu Z C, Wen X G 2010 Phys. Rev. B 82 155138Google Scholar

    [17]

    Luo Z H, Li J, Li Z K, Hung L Y, Wan Y D, Peng X H, Du J F 2018 Nat. Phys. 14 160Google Scholar

    [18]

    Farhi E, Goldstone J, Gutmann S, Sipser M 2000 arXiv: 0001106v1 [quant-ph]

    [19]

    Long G L 2006 Commun. Math. Phys. 45 825

    [20]

    Ladd T D, Jelezko F, Laflamme R, Nakamura Y, Monroe C, O’Brien J L 2010 Nature 464 45Google Scholar

    [21]

    周晓祺 2008 博士学位论文 (合肥: 中国科学技术大学)

    Zhou X Q 2008 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)

    [22]

    Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910Google Scholar

    [23]

    Raussendorf R, Browne D E, Briegel H J 2003 Phys. Rev. A 68 022312Google Scholar

    [24]

    Bouchet A 1993 Discrete Math. 114 75Google Scholar

    [25]

    Fujii K 2015 arXiv: 1504.01444v1 [quant-ph]

    [26]

    Varnava M, Browne D E, Rudolph T 2006 Phys. Rev. Lett. 97 120501Google Scholar

    [27]

    Zhao Z, Chen Y A, Zhang A N, Yang T, Briegel H J, Pan J W 2004 Nature 430 54Google Scholar

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出版历程
  • 收稿日期:  2019-01-24
  • 修回日期:  2019-03-26
  • 上网日期:  2019-06-01
  • 刊出日期:  2019-06-05

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