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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.
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Keywords:
- quantum computation /
- graph state /
- quantum algorithm
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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
Figure 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(k ≠ i); (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
Figure 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
Figure 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
Figure 4. Physical realization of preparing arbitrary quantum state cooperated by two participants in optics.
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[1] Feynman R P 1982 Int. J. Theor. Phys. 21 467
Google Scholar
[2] Benioff P 1980 J. Stat. Phys. 22 563
Google Scholar
[3] Deutsch D 1985 Proc. R. Soc. Lond. A 400 97
Google Scholar
[4] [5] Grover L K 1997 Phys. Rev. Lett. 79 325
Google Scholar
[6] Aspuru-Guzik A, Dutoi A D, Love P J, Head-Gordon M 2005 Science 309 1704
Google Scholar
[7] Jordan S P, Lee K S M, Preskill J 2012 Science 336 1130
Google 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 230501
Google Scholar
[10] Li Z K, Liu X M, Xu N Y, Du J F 2015 Phys. Rev. Lett. 114 140504
Google 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. 11 361
Google 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. 12 534
Google Scholar
[13] Deutsch D E 1989 Proc. R. Soc. Lond. A 425 73
Google Scholar
[14] Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188
Google Scholar
[15] Walther P, Resch K J, Rudolph T, Schenck E, Weinfurter H, Vedral V, Aspelmeyer M, Zeilinger A 2005 Nature 434 169
Google Scholar
[16] Chen X, Gu Z C, Wen X G 2010 Phys. Rev. B 82 155138
Google 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. 14 160
Google 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 45
Google 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. 86 910
Google Scholar
[23] Raussendorf R, Browne D E, Briegel H J 2003 Phys. Rev. A 68 022312
Google Scholar
[24] Bouchet A 1993 Discrete Math. 114 75
Google Scholar
[25] [26] Varnava M, Browne D E, Rudolph T 2006 Phys. Rev. Lett. 97 120501
Google Scholar
[27] Zhao Z, Chen Y A, Zhang A N, Yang T, Briegel H J, Pan J W 2004 Nature 430 54
Google Scholar
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