基于测量的量子计算研究进展

张诗豪; 张向东; 李绿周

doi:10.7498/aps.70.20210923

摘要

相比于量子门电路模型, 基于测量的量子计算模型为实现普适量子计算提供了另一途径, 且经过近二十年的发展其内涵已得到了极大丰富. 本文对基于测量的量子计算模型的研究历史和现状进行综述. 首先简要介绍该模型的基本理论, 包括量子图态等资源态的概念和工作原理、模型的计算普适性和经典模拟方法、在相关量子信息处理领域的应用等. 接着从量子物理特性的角度概括基于测量的量子计算模型和量子多体系统之间的紧密联系, 包括量子纠缠、互文性、量子关联、对称保护拓扑序和量子物质相等作为计算资源所发挥的独特作用. 然后, 总结实现基于测量的量子计算模型的不同技术路线和实验成果. 这些理论和实验方面的进展是不断推动可扩展容错量子计算机研制的力量源泉. 最后, 对该领域未来的研究方向进行讨论和展望, 希望能启发读者进一步学习和探索相关课题.

关键词:

Abstract

Compared with the quantum gate circuit model, the measurement-based quantum computing model provides an alternative way to realize universal quantum computation, and relevant contents have been greatly enriched after nearly two decades of research and exploration. In this article, we review the research history and status of the measurement-based quantum computing model. First, we briefly introduce the basic theories of this model, including the concept and working principles of quantum graph states as resource states, the model’s computational universality and classical simulation methods, and relevant applications in the field of quantum information processing such as designing quantum algorithms and fault-tolerant error correction schemes. Then, from the perspective of quantum physical properties, which include the specific roles of quantum entanglement, contextuality, quantum correlations, symmetry-protected topological order, and quantum phases of matter as computing resources, the close relationship between measurement-based quantum computing model and quantum many-body system is presented. For example, a type of measurement-based computing model for exploiting quantum correlations can show a quantum advantage over the classical local hidden variable models, or certain symmetry-protected topological order states enable the universal quantum computation to be conducted by using only the measurements of single-qubit Pauli operators. Next, a variety of different technical routes and experimental progress of realizing the measurement-based quantum computing model are summarized, such as photonic systems, ion traps, superconducting circuits, etc. These achievements in various physical areas lay the foundation for future scalable and fault-tolerant quantum computers. Finally, we discuss and prospect the future research directions in this field thereby inspiring readers to further study and explore the relevant subjects.

Keywords:

作者及机构信息

1.
中山大学计算机学院, 量子计算与计算机理论研究所, 广州　510006

2.
北京理工大学物理学院, 先进光电量子结构设计与测量教育部重点实验室, 北京　100081

通信作者: 李绿周, lilvzh@mail.sysu.edu.cn

基金项目: 国家自然科学基金(批准号: 61772565, 62102464)、广东省基础与应用基础研究基金(批准号: 2020B1515020050)、广东省重点研发项目(批准号: 2018B030325001)和中国博士后科学基金(批准号: 2020M683049, 2021T140761)资助的课题

Authors and contacts

1.
Institute of Quantum Computing and Computer Theory, School of Computer Science and Engineering, Sun Yat-Sen University, Guangzhou 510006, China

2.
Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China

Corresponding author: Li Lü-Zhou, lilvzh@mail.sysu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61772565, 62102464), the Guangdong Basic and Applied Basic Research Foundation, China (Grant No. 2020B1515020050), the Key Research and Development project of Guangdong Province, China (Grant No. 2018B030325001), and the China Postdoctoral Science Foundation (Grant Nos. 2020M683049, 2021T140761)

文章全文 : translate this paragraph

参考文献

[1]	Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (New York: Cambridge University Press) pp1−12
[2]	Barenco A, Bennett C H, Cleve R, DiVincenzo D P, Margolus N, Shor P, Sleator T, Smolin J A, Weinfurter H 1995 Phys. Rev. A 52 3457 Google Scholar
[3]	Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188 Google Scholar
[4]	Raussendorf R, Browne D E, Briegel H J 2003 Phys. Rev. A 68 022312 Google Scholar
[5]	Prevedel R, Walther P, Tiefenbacher F, Böhi P, Kaltenbaek R, Jennewein T, Zeilinger A 2007 Nature 445 65 Google Scholar
[6]	Lanyon B, Jurcevic P, Zwerger M, Hempel C, Martinez E, Dür W, Briegel H, Blatt R, Roos C F 2013 Phys. Rev. Lett. 111 210501 Google Scholar
[7]	Tame M, Özdemir Ş, Koashi M, Imoto N, Kim M 2009 Phys. Rev. A 79 020302 Google Scholar
[8]	Tame M S, Prevedel R, Paternostro M, Böhi P, Kim M, Zeilinger A 2007 Phys. Rev. Lett. 98 140501 Google Scholar
[9]	Tame M, Kim M 2010 Phys. Rev. A 82 030305 Google Scholar
[10]	Tame M S, Bell B A, Di Franco C, Wadsworth W J, Rarity J G 2014 Phys. Rev. Lett. 113 200501 Google Scholar
[11]	Bell B, Herrera-Martí D, Tame M, Markham D, Wadsworth W, Rarity J 2014 Nat. Commun. 5 3658 Google Scholar
[12]	Pathumsoot P, Matsuo T, Satoh T, Hajdušek M, Suwanna S, Van Meter R 2020 Phys. Rev. A 101 052301 Google Scholar
[13]	Hein M, Eisert J, Briegel H J 2004 Phys. Rev. A 69 062311 Google Scholar
[14]	Briegel H J, Browne D E, Dür W, Raussendorf R, Van den Nest M 2009 Nat. Phys. 5 19 Google Scholar
[15]	Preskill J 2018 Quantum 2 79 Google Scholar
[16]	Gühne O, Tóth G 2009 Phys. Rep. 474 1 Google Scholar
[17]	Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 Google Scholar
[18]	Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575 Google Scholar
[19]	Gottesman D, Chuang I L 1999 Nature 402 390 Google Scholar
[20]	Perdrix S 2005 Int. J. Quantum Inf. 3 219 Google Scholar
[21]	Jorrand P, Perdrix S 2005 Proc. SPIE 5833 44 Google Scholar
[22]	Gross D, Eisert J 2007 Phys. Rev. Lett. 98 220503 Google Scholar
[23]	Gross D, Eisert J, Schuch N, Perez-Garcia D 2007 Phys. Rev. A 76 052315 Google Scholar
[24]	Danos V, Kashefi E 2006 Phys. Rev. A 74 052310 Google Scholar
[25]	van den Nest M, Dür W, Miyake A, Briegel H 2007 New J. Phys. 9 204 Google Scholar
[26]	Danos V, Kashefi E, Panangaden P 2007 J. ACM 54 8 Google Scholar
[27]	Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910 Google Scholar
[28]	Hein M, Dür W, Eisert J, Raussendorf R, Nest M, Briegel H J 2006 arXiv: 0602096 [quant-ph]
[29]	Walther P, Resch K J, Rudolph T, et al. 2005 Nature 434 169 Google Scholar
[30]	Lu C Y, Zhou X Q, Gühne O, Gao W B, Zhang J, Yuan Z S, Goebel A, Yang T, Pan J W 2007 Nat. Phys. 3 91 Google Scholar
[31]	Van den Nest M, Miyake A, Dür W, Briegel H J 2006 Phys. Rev. Lett. 97 150504 Google Scholar
[32]	Nielsen M A 2006 Rep. Math. Phys. 57 147 Google Scholar
[33]	Browne D E, Rudolph T 2005 Phys. Rev. Lett. 95 010501 Google Scholar
[34]	Bell B, Tame M, Clark A, Nock R, Wadsworth W, Rarity J G 2013 New J. Phys. 15 053030 Google Scholar
[35]	Leung D W 2004 Int. J. Quantum Inf. 2 33 Google Scholar
[36]	Aliferis P, Leung D W 2004 Phys. Rev. A 70 062314 Google Scholar
[37]	Childs A M, Leung D W, Nielsen M A 2005 Phys. Rev. A 71 032318 Google Scholar
[38]	Verstraete F, Cirac J I 2004 Phys. Rev. A 70 060302 Google Scholar
[39]	Nielsen M A 2004 Phys. Rev. Lett. 93 040503 Google Scholar
[40]	Zwerger M, Briegel H, Dür W 2014 Sci. Rep. 4 5364 Google Scholar
[41]	Vidal G 2003 Phys. Rev. Lett. 91 147902 Google Scholar
[42]	Markov I L, Shi Y 2008 SIAM J. Comput. 38 963 Google Scholar
[43]	Jozsa R 2006 arXiv: 0603163 [quant-ph]
[44]	Shi Y Y, Duan L M, Vidal G 2006 Phys. Rev. A 74 022320 Google Scholar
[45]	van den Nest M, Dür W, Vidal G, Briegel H J 2007 Phys. Rev. A 75 012337 Google Scholar
[46]	Yoran N, Short A J 2006 Phys. Rev. Lett. 96 170503 Google Scholar
[47]	Bravyi S, Raussendorf R 2007 Phys. Rev. A 76 022304 Google Scholar
[48]	Zhang S, Zhang Y, Sun Y, Sun H, Zhang X 2019 Opt. Express 27 436 Google Scholar
[49]	Chen M C, Li R, Gan L, Zhu X, Yang G, Lu C Y, Pan J W 2020 Phys. Rev. Lett. 124 080502 Google Scholar
[50]	Chen K, Li C M, Zhang Q, Chen Y A, Goebel A, Chen S, Mair A, Pan J W 2007 Phys. Rev. Lett. 99 120503 Google Scholar
[51]	Raussendorf R 2013 Phys. Rev. A 88 022322 Google Scholar
[52]	Oestereich A L, Galvão E F 2017 Phys. Rev. A 96 062305 Google Scholar
[53]	Raussendorf R, Briegel H J 2002 Quantum Inf. Comput. 2 443
[54]	Broadbent A, Kashefi E 2009 Theor. Comput. Sci. 410 2489 Google Scholar
[55]	Browne D, Kashefi E, Perdrix S 2010 Conference on Quantum Computation, Communication, and Cryptography Leeds, UK, April 2010 pp35−46
[56]	Raussendorf R 2003 Ph. D. Dissertation (Munich: LMU)
[57]	Nielsen M A, Dawson C M 2005 Phys. Rev. A 71 042323 Google Scholar
[58]	Dawson C M, Haselgrove H L, Nielsen M A 2006 Phys. Rev. Lett. 96 020501 Google Scholar
[59]	Raussendorf R, Harrington J, Goyal K 2006 Ann. Phys. 321 2242 Google Scholar
[60]	Raussendorf R, Harrington J, Goyal K 2007 New J. Phys. 9 199 Google Scholar
[61]	Raussendorf R, Harrington J 2007 Phys. Rev. Lett. 98 190504 Google Scholar
[62]	Devitt S J, Fowler A G, Stephens A M, Greentree A D, Hollenberg L C, Munro W J, Nemoto K 2009 New J. Phys. 11 083032 Google Scholar
[63]	Herrera-Martí D A, Fowler A G, Jennings D, Rudolph T 2010 Phys. Rev. A 82 032332 Google Scholar
[64]	Yao X C, Wang T X, Chen H Z, et al. 2012 Nature 482 489 Google Scholar
[65]	Fukui K, Asavanant W, Furusawa A 2020 Phys. Rev. A 102 032614 Google Scholar
[66]	Broadbent A, Fitzsimons J, Kashefi E 2009 Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science pp517−526
[67]	Barz S, Kashefi E, Broadbent A, Fitzsimons J F, Zeilinger A, Walther P 2012 Science 335 303 Google Scholar
[68]	田宇玲, 冯田峰, 周晓祺 2019 物理学报 68 110302 Google Scholar Tian Y L, Feng T F, Zhou X Q 2019 Acta Phys. Sin. 68 110302 Google Scholar
[69]	Prevedel R, Stefanov A, Walther P, Zeilinger A 2007 New J. Phys. 9 205 Google Scholar
[70]	Azuma K, Tamaki K, Lo H K 2015 Nat. Commun. 6 6787 Google Scholar
[71]	Matsuo T, Satoh T, Nagayama S, Van Meter R 2018 Phys. Rev. A 97 062328 Google Scholar
[72]	van den Nest M, Dür W, Briegel H J 2008 Phys. Rev. Lett. 100 110501 Google Scholar
[73]	de las Cuevas G, Cubitt T S 2016 Science 351 1180 Google Scholar
[74]	Bermejo-Vega J, Hangleiter D, Schwarz M, Raussendorf R, Eisert J 2018 Phys. Rev. X 8 021010 Google Scholar
[75]	Miller J, Miyake A 2016 npj Quantum Inform. 2 16036 Google Scholar
[76]	Demirel B, Weng W, Thalacker C, Hoban M, Barz S 2021 npj Quantum Inform. 7 29 Google Scholar
[77]	Chen X, Zeng B, Gu Z C, Yoshida B, Chuang I L 2009 Phys. Rev. Lett. 102 220501 Google Scholar
[78]	Cai J, Miyake A, Dür W, Briegel H J 2010 Phys. Rev. A 82 052309 Google Scholar
[79]	Chen J, Chen X, Duan R, Ji Z, Zeng B 2011 Phys. Rev. A 83 050301 Google Scholar
[80]	Cai J M, Dür W, van den Nest M, Miyake A, Briegel H 2009 Phys. Rev. Lett. 103 050503 Google Scholar
[81]	Rossi M, Huber M, Bruß D, Macchiavello C 2013 New J. Phys. 15 113022 Google Scholar
[82]	Qu R, Wang J, Li Z S, Bao Y R 2013 Phys. Rev. A 87 022311 Google Scholar
[83]	Gachechiladze M, Budroni C, Gühne O 2016 Phys. Rev. Lett. 116 070401 Google Scholar
[84]	Gross D, Flammia S T, Eisert J 2009 Phys. Rev. Lett. 102 190501 Google Scholar
[85]	Bremner M J, Mora C, Winter A 2009 Phys. Rev. Lett. 102 190502 Google Scholar
[86]	Morimae T 2017 Phys. Rev. A 96 052308 Google Scholar
[87]	Brunner N, Cavalcanti D, Pironio S, Scarani V, Wehner S 2014 Rev. Mod. Phys. 86 419 Google Scholar
[88]	Howard M, Wallman J, Veitch V, Emerson J 2014 Nature 510 351 Google Scholar
[89]	Anders J, Browne D E 2009 Phys. Rev. Lett. 102 050502 Google Scholar
[90]	Hoban M J, Wallman J J, Anwar H, Usher N, Raussendorf R, Browne D E 2014 Phys. Rev. Lett. 112 140505 Google Scholar
[91]	Hoban M J, Campbell E T, Loukopoulos K, Browne D E 2011 New J. Phys. 13 023014 Google Scholar
[92]	Abramsky S, Barbosa R S, Mansfield S 2017 Phys. Rev. Lett. 119 050504 Google Scholar
[93]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[94]	Gu Z C, Wen X G 2009 Phys. Rev. B 80 155131 Google Scholar
[95]	Pollmann F, Berg E, Turner A M, Oshikawa M 2012 Phys. Rev. B 85 075125 Google Scholar
[96]	Chen X, Gu Z C, Liu Z X, Wen X G 2012 Science 338 1604 Google Scholar
[97]	Chen X, Gu Z C, Liu Z X, Wen X G 2013 Phys. Rev. B 87 155114 Google Scholar
[98]	Else D V, Schwarz I, Bartlett S D, Doherty A C 2012 Phys. Rev. Lett. 108 240505 Google Scholar
[99]	Miller J, Miyake A 2015 Phys. Rev. Lett. 114 120506 Google Scholar
[100]	Raussendorf R, Wang D S, Prakash A, Wei T C, Stephen D T 2017 Phys. Rev. A 96 012302 Google Scholar
[101]	Nautrup H P, Wei T C 2015 Phys. Rev. A 92 052309 Google Scholar
[102]	Chen Y, Prakash A, Wei T C 2018 Phys. Rev. A 97 022305 Google Scholar
[103]	Raussendorf R, Okay C, Wang D S, Stephen D T, Nautrup H P 2019 Phys. Rev. Lett. 122 090501 Google Scholar
[104]	Stephen D T, Nautrup H P, Bermejo-Vega J, Eisert J, Raussendorf R 2019 Quantum 3 142 Google Scholar
[105]	Daniel A K, Alexander R N, Miyake A 2020 Quantum 4 228 Google Scholar
[106]	Choo K, Von Keyserlingk C, Regnault N, Neupert T 2018 Phys. Rev. Lett. 121 086808 Google Scholar
[107]	Azses D, Haenel R, Naveh Y, Raussendorf R, Sela E, Dalla Torre E G 2020 Phys. Rev. Lett. 125 120502 Google Scholar
[108]	Tokunaga Y, Kuwashiro S, Yamamoto T, Koashi M, Imoto N 2008 Phys. Rev. Lett. 100 210501 Google Scholar
[109]	Gao W B, Xu P, Yao X C, et al. 2010 Phys. Rev. Lett. 104 020501 Google Scholar
[110]	Vallone G, Pomarico E, De Martini F, Mataloni P 2008 Phys. Rev. A 78 042335 Google Scholar
[111]	Barz S, Vasconcelos R, Greganti C, Zwerger M, Dür W, Briegel H J, Walther P 2014 Phys. Rev. A 90 042302 Google Scholar
[112]	Gao W B, Yao X C, Cai J M, Lu H, Xu P, Yang T, Lu C Y, Chen Y A, Chen Z B, Pan J W 2011 Nat. Photonics 5 117 Google Scholar
[113]	Reimer C, Sciara S, Roztocki P, et al. 2019 Nat. Phys. 15 148 Google Scholar
[114]	Ciampini M A, Orieux A, Paesani S, et al. 2016 Light Sci. Appl. 5 e16064 Google Scholar
[115]	Adcock J C, Vigliar C, Santagati R, Silverstone J W, Thompson M G 2019 Nat. Commun. 10 3528 Google Scholar
[116]	Knill E, Laflamme R, Milburn G J 2001 Nature 409 46 Google Scholar
[117]	Huang Y F, Ren X F, Zhang Y S, Duan L M, Guo G C 2004 Phys. Rev. Lett. 93 240501 Google Scholar
[118]	Xiang G Y, Li J, Guo G C 2005 Phys. Rev. A 71 044304 Google Scholar
[119]	Gao W B, Goebel A M, Lu C Y, et al. 2010 P. Nalt. Acad. Sci. 107 20869 Google Scholar
[120]	Su X, Tan A, Jia X, Zhang J, Xie C, Peng K 2007 Phys. Rev. Lett. 98 070502 Google Scholar
[121]	Su X, Hao S, Deng X, Ma L, Wang M, Jia X, Xie C, Peng K 2013 Nat. Commun. 4 2828 Google Scholar
[122]	Su X, Jia X, Xie C, Peng K 2014 Sci. China Phys. Mech. 57 1210 Google Scholar
[123]	Qin Z, Gessner M, Ren Z, Deng X, Han D, Li W, Su X, Smerzi A, Peng K 2019 NPJ Quantum Inf. 5 3 Google Scholar
[124]	Ukai R, Iwata N, Shimokawa Y, et al. 2011 Phys. Rev. Lett. 106 240504 Google Scholar
[125]	Yokoyama S, Ukai R, Armstrong S C, et al. 2013 Nat. Photonics 7 982 Google Scholar
[126]	Yoshikawa J I, Yokoyama S, Kaji T, et al. 2016 APL Photonics 1 060801 Google Scholar
[127]	Cirac J I, Zoller P 1995 Phys. Rev. Lett. 74 4091 Google Scholar
[128]	Wunderlich H, Wunderlich C, Singer K, Schmidt-Kaler F 2009 Phys. Rev. A 79 052324 Google Scholar
[129]	Stock R, James D F 2009 Phys. Rev. Lett. 102 170501 Google Scholar
[130]	Lanyon B P, Zwerger M, Jurcevic P, Hempel C, Dür W, Briegel H J, Blatt R, Roos C 2014 Phys. Rev. Lett. 112 100403 Google Scholar
[131]	You J, Wang X B, Tanamoto T, Nori F 2007 Phys. Rev. A 75 052319 Google Scholar
[132]	Zhang X, Gao K, Feng M 2006 Phys. Rev. A 74 024303 Google Scholar
[133]	Xue Z Y, Wang Z 2007 Phys. Rev. A 75 064303 Google Scholar
[134]	Xue Z Y, Zhang G, Dong P, Yi Y M, Cao Z L 2006 Eur. Phys. J. B 52 333 Google Scholar
[135]	Gong M, Chen M C, Zheng Y, et al. 2019 Phys. Rev. Lett. 122 110501 Google Scholar
[136]	Mooney G J, Hill C D, Hollenberg L C 2019 Sci. Rep. 9 13465 Google Scholar
[137]	Albarrán-Arriagada F, Barrios G A, Sanz M, et al. 2018 Phys. Rev. A 97 032320 Google Scholar
[138]	Vaucher B, Nunnenkamp A, Jaksch D 2008 New J. Phys. 10 023005 Google Scholar
[139]	Mamaev M, Blatt R, Ye J, Rey A M 2019 Phys. Rev. Lett. 122 160402 Google Scholar
[140]	Economou S E, Lindner N, Rudolph T 2010 Phys. Rev. Lett. 105 093601 Google Scholar
[141]	Gimeno-Segovia M, Rudolph T, Economou S E 2019 Phys. Rev. Lett. 123 070501 Google Scholar
[142]	Ju C, Zhu J, Peng X, Chong B, Zhou X, Du J 2010 Phys. Rev. A 81 012322 Google Scholar
[143]	Blythe P, Varcoe B 2006 New J. Phys. 8 231 Google Scholar
[144]	Takeuchi Y, Morimae T, Hayashi M 2019 Sci. Rep. 9 13585 Google Scholar
[145]	Gachechiladze M, Gühne O, Miyake A 2019 Phys. Rev. A 99 052304 Google Scholar
[146]	Mansfield S, Kashefi E 2018 Phys. Rev. Lett. 121 230401 Google Scholar
[147]	Frembs M, Roberts S, Bartlett S D 2018 New J. Phys. 20 103011 Google Scholar
[148]	Hu F, Lamata L, Wang C, Chen X, Solano E, Sanz M 2020 Phys. Rev. Appl. 13 054062 Google Scholar
[149]	Yan S, Qi H, Cui W 2020 Phys. Rev. A 102 052421 Google Scholar
[150]	Devakul T, Williamson D J 2018 Phys. Rev. A 98 022332 Google Scholar
[151]	Wei T C, Affleck I, Raussendorf R 2011 Phys. Rev. Lett. 106 070501 Google Scholar

施引文献

图 1 不同类型的图态　(a)线性簇态; (b)星形图态; (c)马蹄形簇态; (d)可扩展的二维方格图态

Fig. 1. Different types of graph states: (a) A linear cluster state; (b) a star-graph state; (c) a horseshoe cluster state; (d) the scalable 2D square graph state.

下载: 全尺寸图片幻灯片

图 2 单向量子计算执行量子门操作　(a)输入态$ \left| + \right\rangle $经过${R_z}( - \alpha )$旋转和Hadamard门作用; (b)以测量纠缠态的方式等价地实现(a); (c)为(b)的扩展, 制备并测量4-qubit线性簇态以实现任意的单量子比特旋转门; (d)以4-qubit星形簇态执行CNOT门

Fig. 2. Realization of quantum gates in the 1 WQC model: (a) Input state $ \left| + \right\rangle $ undergoes a ${R_z}( - \alpha )$ rotation and a Hadamard gate; (b) a circuit equivalent to (a) by measuring an entangled state; (c) a generalization of (b) to prepare and measure a 4-qubit linear cluster state for implementing arbitrary single-qubit rotation gates; (d) a circuit performing the CNOT gate via a star cluster state.

下载: 全尺寸图片幻灯片

图 3 基于传态的方案实现单量子比特门　(a)一方远程制备态$U\left| \alpha \right\rangle $并通过Bell测量和泡利修正传给另一方, 注意U和Bell测量可以直接合并成新的联合测量; (b)利用制备好的资源态$(I \otimes U)\left| {{\beta _{{\text{00}}}}} \right\rangle $来间接执行$U\left| \alpha \right\rangle $

Fig. 3. Teleportation-based scheme for implementing any sing-qubit gate: (a) State $U\left| \alpha \right\rangle $is remotely prepared at one site and teleported to another site via Bell measurement and Pauli corrections, note here U and Bell measurement can be directly combined into a new joint measurement; (b) the scheme to indirectly implement $U\left| \alpha \right\rangle $ via a prepared resource state $(I \otimes U)\left| {{\beta _{{\text{00}}}}} \right\rangle $.

下载: 全尺寸图片幻灯片

图 4 利用关联的计算模型. 经典控制计算机提供k个测量设置中的1个作为对关联多方资源态中个体的经典输入(蓝色箭头), 并且接收l个测量结果中的1个(红色箭头)作为输出

Fig. 4. A computational model exploiting correlations. The classical control computer provides one of k measurement settings as the classical input (blue arrows) to each of the parties in the correlated resource state and receives one of l possible measurement results (red arrows) as the output.

下载: 全尺寸图片幻灯片

[1]	Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (New York: Cambridge University Press) pp1−12
[2]	Barenco A, Bennett C H, Cleve R, DiVincenzo D P, Margolus N, Shor P, Sleator T, Smolin J A, Weinfurter H 1995 Phys. Rev. A 52 3457 Google Scholar
[3]	Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188 Google Scholar
[4]	Raussendorf R, Browne D E, Briegel H J 2003 Phys. Rev. A 68 022312 Google Scholar
[5]	Prevedel R, Walther P, Tiefenbacher F, Böhi P, Kaltenbaek R, Jennewein T, Zeilinger A 2007 Nature 445 65 Google Scholar
[6]	Lanyon B, Jurcevic P, Zwerger M, Hempel C, Martinez E, Dür W, Briegel H, Blatt R, Roos C F 2013 Phys. Rev. Lett. 111 210501 Google Scholar
[7]	Tame M, Özdemir Ş, Koashi M, Imoto N, Kim M 2009 Phys. Rev. A 79 020302 Google Scholar
[8]	Tame M S, Prevedel R, Paternostro M, Böhi P, Kim M, Zeilinger A 2007 Phys. Rev. Lett. 98 140501 Google Scholar
[9]	Tame M, Kim M 2010 Phys. Rev. A 82 030305 Google Scholar
[10]	Tame M S, Bell B A, Di Franco C, Wadsworth W J, Rarity J G 2014 Phys. Rev. Lett. 113 200501 Google Scholar
[11]	Bell B, Herrera-Martí D, Tame M, Markham D, Wadsworth W, Rarity J 2014 Nat. Commun. 5 3658 Google Scholar
[12]	Pathumsoot P, Matsuo T, Satoh T, Hajdušek M, Suwanna S, Van Meter R 2020 Phys. Rev. A 101 052301 Google Scholar
[13]	Hein M, Eisert J, Briegel H J 2004 Phys. Rev. A 69 062311 Google Scholar
[14]	Briegel H J, Browne D E, Dür W, Raussendorf R, Van den Nest M 2009 Nat. Phys. 5 19 Google Scholar
[15]	Preskill J 2018 Quantum 2 79 Google Scholar
[16]	Gühne O, Tóth G 2009 Phys. Rep. 474 1 Google Scholar
[17]	Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 Google Scholar
[18]	Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575 Google Scholar
[19]	Gottesman D, Chuang I L 1999 Nature 402 390 Google Scholar
[20]	Perdrix S 2005 Int. J. Quantum Inf. 3 219 Google Scholar
[21]	Jorrand P, Perdrix S 2005 Proc. SPIE 5833 44 Google Scholar
[22]	Gross D, Eisert J 2007 Phys. Rev. Lett. 98 220503 Google Scholar
[23]	Gross D, Eisert J, Schuch N, Perez-Garcia D 2007 Phys. Rev. A 76 052315 Google Scholar
[24]	Danos V, Kashefi E 2006 Phys. Rev. A 74 052310 Google Scholar
[25]	van den Nest M, Dür W, Miyake A, Briegel H 2007 New J. Phys. 9 204 Google Scholar
[26]	Danos V, Kashefi E, Panangaden P 2007 J. ACM 54 8 Google Scholar
[27]	Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910 Google Scholar
[28]	Hein M, Dür W, Eisert J, Raussendorf R, Nest M, Briegel H J 2006 arXiv: 0602096 [quant-ph]
[29]	Walther P, Resch K J, Rudolph T, et al. 2005 Nature 434 169 Google Scholar
[30]	Lu C Y, Zhou X Q, Gühne O, Gao W B, Zhang J, Yuan Z S, Goebel A, Yang T, Pan J W 2007 Nat. Phys. 3 91 Google Scholar
[31]	Van den Nest M, Miyake A, Dür W, Briegel H J 2006 Phys. Rev. Lett. 97 150504 Google Scholar
[32]	Nielsen M A 2006 Rep. Math. Phys. 57 147 Google Scholar
[33]	Browne D E, Rudolph T 2005 Phys. Rev. Lett. 95 010501 Google Scholar
[34]	Bell B, Tame M, Clark A, Nock R, Wadsworth W, Rarity J G 2013 New J. Phys. 15 053030 Google Scholar
[35]	Leung D W 2004 Int. J. Quantum Inf. 2 33 Google Scholar
[36]	Aliferis P, Leung D W 2004 Phys. Rev. A 70 062314 Google Scholar
[37]	Childs A M, Leung D W, Nielsen M A 2005 Phys. Rev. A 71 032318 Google Scholar
[38]	Verstraete F, Cirac J I 2004 Phys. Rev. A 70 060302 Google Scholar
[39]	Nielsen M A 2004 Phys. Rev. Lett. 93 040503 Google Scholar
[40]	Zwerger M, Briegel H, Dür W 2014 Sci. Rep. 4 5364 Google Scholar
[41]	Vidal G 2003 Phys. Rev. Lett. 91 147902 Google Scholar
[42]	Markov I L, Shi Y 2008 SIAM J. Comput. 38 963 Google Scholar
[43]	Jozsa R 2006 arXiv: 0603163 [quant-ph]
[44]	Shi Y Y, Duan L M, Vidal G 2006 Phys. Rev. A 74 022320 Google Scholar
[45]	van den Nest M, Dür W, Vidal G, Briegel H J 2007 Phys. Rev. A 75 012337 Google Scholar
[46]	Yoran N, Short A J 2006 Phys. Rev. Lett. 96 170503 Google Scholar
[47]	Bravyi S, Raussendorf R 2007 Phys. Rev. A 76 022304 Google Scholar
[48]	Zhang S, Zhang Y, Sun Y, Sun H, Zhang X 2019 Opt. Express 27 436 Google Scholar
[49]	Chen M C, Li R, Gan L, Zhu X, Yang G, Lu C Y, Pan J W 2020 Phys. Rev. Lett. 124 080502 Google Scholar
[50]	Chen K, Li C M, Zhang Q, Chen Y A, Goebel A, Chen S, Mair A, Pan J W 2007 Phys. Rev. Lett. 99 120503 Google Scholar
[51]	Raussendorf R 2013 Phys. Rev. A 88 022322 Google Scholar
[52]	Oestereich A L, Galvão E F 2017 Phys. Rev. A 96 062305 Google Scholar
[53]	Raussendorf R, Briegel H J 2002 Quantum Inf. Comput. 2 443
[54]	Broadbent A, Kashefi E 2009 Theor. Comput. Sci. 410 2489 Google Scholar
[55]	Browne D, Kashefi E, Perdrix S 2010 Conference on Quantum Computation, Communication, and Cryptography Leeds, UK, April 2010 pp35−46
[56]	Raussendorf R 2003 Ph. D. Dissertation (Munich: LMU)
[57]	Nielsen M A, Dawson C M 2005 Phys. Rev. A 71 042323 Google Scholar
[58]	Dawson C M, Haselgrove H L, Nielsen M A 2006 Phys. Rev. Lett. 96 020501 Google Scholar
[59]	Raussendorf R, Harrington J, Goyal K 2006 Ann. Phys. 321 2242 Google Scholar
[60]	Raussendorf R, Harrington J, Goyal K 2007 New J. Phys. 9 199 Google Scholar
[61]	Raussendorf R, Harrington J 2007 Phys. Rev. Lett. 98 190504 Google Scholar
[62]	Devitt S J, Fowler A G, Stephens A M, Greentree A D, Hollenberg L C, Munro W J, Nemoto K 2009 New J. Phys. 11 083032 Google Scholar
[63]	Herrera-Martí D A, Fowler A G, Jennings D, Rudolph T 2010 Phys. Rev. A 82 032332 Google Scholar
[64]	Yao X C, Wang T X, Chen H Z, et al. 2012 Nature 482 489 Google Scholar
[65]	Fukui K, Asavanant W, Furusawa A 2020 Phys. Rev. A 102 032614 Google Scholar
[66]	Broadbent A, Fitzsimons J, Kashefi E 2009 Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science pp517−526
[67]	Barz S, Kashefi E, Broadbent A, Fitzsimons J F, Zeilinger A, Walther P 2012 Science 335 303 Google Scholar
[68]	田宇玲, 冯田峰, 周晓祺 2019 物理学报 68 110302 Google Scholar Tian Y L, Feng T F, Zhou X Q 2019 Acta Phys. Sin. 68 110302 Google Scholar
[69]	Prevedel R, Stefanov A, Walther P, Zeilinger A 2007 New J. Phys. 9 205 Google Scholar
[70]	Azuma K, Tamaki K, Lo H K 2015 Nat. Commun. 6 6787 Google Scholar
[71]	Matsuo T, Satoh T, Nagayama S, Van Meter R 2018 Phys. Rev. A 97 062328 Google Scholar
[72]	van den Nest M, Dür W, Briegel H J 2008 Phys. Rev. Lett. 100 110501 Google Scholar
[73]	de las Cuevas G, Cubitt T S 2016 Science 351 1180 Google Scholar
[74]	Bermejo-Vega J, Hangleiter D, Schwarz M, Raussendorf R, Eisert J 2018 Phys. Rev. X 8 021010 Google Scholar
[75]	Miller J, Miyake A 2016 npj Quantum Inform. 2 16036 Google Scholar
[76]	Demirel B, Weng W, Thalacker C, Hoban M, Barz S 2021 npj Quantum Inform. 7 29 Google Scholar
[77]	Chen X, Zeng B, Gu Z C, Yoshida B, Chuang I L 2009 Phys. Rev. Lett. 102 220501 Google Scholar
[78]	Cai J, Miyake A, Dür W, Briegel H J 2010 Phys. Rev. A 82 052309 Google Scholar
[79]	Chen J, Chen X, Duan R, Ji Z, Zeng B 2011 Phys. Rev. A 83 050301 Google Scholar
[80]	Cai J M, Dür W, van den Nest M, Miyake A, Briegel H 2009 Phys. Rev. Lett. 103 050503 Google Scholar
[81]	Rossi M, Huber M, Bruß D, Macchiavello C 2013 New J. Phys. 15 113022 Google Scholar
[82]	Qu R, Wang J, Li Z S, Bao Y R 2013 Phys. Rev. A 87 022311 Google Scholar
[83]	Gachechiladze M, Budroni C, Gühne O 2016 Phys. Rev. Lett. 116 070401 Google Scholar
[84]	Gross D, Flammia S T, Eisert J 2009 Phys. Rev. Lett. 102 190501 Google Scholar
[85]	Bremner M J, Mora C, Winter A 2009 Phys. Rev. Lett. 102 190502 Google Scholar
[86]	Morimae T 2017 Phys. Rev. A 96 052308 Google Scholar
[87]	Brunner N, Cavalcanti D, Pironio S, Scarani V, Wehner S 2014 Rev. Mod. Phys. 86 419 Google Scholar
[88]	Howard M, Wallman J, Veitch V, Emerson J 2014 Nature 510 351 Google Scholar
[89]	Anders J, Browne D E 2009 Phys. Rev. Lett. 102 050502 Google Scholar
[90]	Hoban M J, Wallman J J, Anwar H, Usher N, Raussendorf R, Browne D E 2014 Phys. Rev. Lett. 112 140505 Google Scholar
[91]	Hoban M J, Campbell E T, Loukopoulos K, Browne D E 2011 New J. Phys. 13 023014 Google Scholar
[92]	Abramsky S, Barbosa R S, Mansfield S 2017 Phys. Rev. Lett. 119 050504 Google Scholar
[93]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[94]	Gu Z C, Wen X G 2009 Phys. Rev. B 80 155131 Google Scholar
[95]	Pollmann F, Berg E, Turner A M, Oshikawa M 2012 Phys. Rev. B 85 075125 Google Scholar
[96]	Chen X, Gu Z C, Liu Z X, Wen X G 2012 Science 338 1604 Google Scholar
[97]	Chen X, Gu Z C, Liu Z X, Wen X G 2013 Phys. Rev. B 87 155114 Google Scholar
[98]	Else D V, Schwarz I, Bartlett S D, Doherty A C 2012 Phys. Rev. Lett. 108 240505 Google Scholar
[99]	Miller J, Miyake A 2015 Phys. Rev. Lett. 114 120506 Google Scholar
[100]	Raussendorf R, Wang D S, Prakash A, Wei T C, Stephen D T 2017 Phys. Rev. A 96 012302 Google Scholar
[101]	Nautrup H P, Wei T C 2015 Phys. Rev. A 92 052309 Google Scholar
[102]	Chen Y, Prakash A, Wei T C 2018 Phys. Rev. A 97 022305 Google Scholar
[103]	Raussendorf R, Okay C, Wang D S, Stephen D T, Nautrup H P 2019 Phys. Rev. Lett. 122 090501 Google Scholar
[104]	Stephen D T, Nautrup H P, Bermejo-Vega J, Eisert J, Raussendorf R 2019 Quantum 3 142 Google Scholar
[105]	Daniel A K, Alexander R N, Miyake A 2020 Quantum 4 228 Google Scholar
[106]	Choo K, Von Keyserlingk C, Regnault N, Neupert T 2018 Phys. Rev. Lett. 121 086808 Google Scholar
[107]	Azses D, Haenel R, Naveh Y, Raussendorf R, Sela E, Dalla Torre E G 2020 Phys. Rev. Lett. 125 120502 Google Scholar
[108]	Tokunaga Y, Kuwashiro S, Yamamoto T, Koashi M, Imoto N 2008 Phys. Rev. Lett. 100 210501 Google Scholar
[109]	Gao W B, Xu P, Yao X C, et al. 2010 Phys. Rev. Lett. 104 020501 Google Scholar
[110]	Vallone G, Pomarico E, De Martini F, Mataloni P 2008 Phys. Rev. A 78 042335 Google Scholar
[111]	Barz S, Vasconcelos R, Greganti C, Zwerger M, Dür W, Briegel H J, Walther P 2014 Phys. Rev. A 90 042302 Google Scholar
[112]	Gao W B, Yao X C, Cai J M, Lu H, Xu P, Yang T, Lu C Y, Chen Y A, Chen Z B, Pan J W 2011 Nat. Photonics 5 117 Google Scholar
[113]	Reimer C, Sciara S, Roztocki P, et al. 2019 Nat. Phys. 15 148 Google Scholar
[114]	Ciampini M A, Orieux A, Paesani S, et al. 2016 Light Sci. Appl. 5 e16064 Google Scholar
[115]	Adcock J C, Vigliar C, Santagati R, Silverstone J W, Thompson M G 2019 Nat. Commun. 10 3528 Google Scholar
[116]	Knill E, Laflamme R, Milburn G J 2001 Nature 409 46 Google Scholar
[117]	Huang Y F, Ren X F, Zhang Y S, Duan L M, Guo G C 2004 Phys. Rev. Lett. 93 240501 Google Scholar
[118]	Xiang G Y, Li J, Guo G C 2005 Phys. Rev. A 71 044304 Google Scholar
[119]	Gao W B, Goebel A M, Lu C Y, et al. 2010 P. Nalt. Acad. Sci. 107 20869 Google Scholar
[120]	Su X, Tan A, Jia X, Zhang J, Xie C, Peng K 2007 Phys. Rev. Lett. 98 070502 Google Scholar
[121]	Su X, Hao S, Deng X, Ma L, Wang M, Jia X, Xie C, Peng K 2013 Nat. Commun. 4 2828 Google Scholar
[122]	Su X, Jia X, Xie C, Peng K 2014 Sci. China Phys. Mech. 57 1210 Google Scholar
[123]	Qin Z, Gessner M, Ren Z, Deng X, Han D, Li W, Su X, Smerzi A, Peng K 2019 NPJ Quantum Inf. 5 3 Google Scholar
[124]	Ukai R, Iwata N, Shimokawa Y, et al. 2011 Phys. Rev. Lett. 106 240504 Google Scholar
[125]	Yokoyama S, Ukai R, Armstrong S C, et al. 2013 Nat. Photonics 7 982 Google Scholar
[126]	Yoshikawa J I, Yokoyama S, Kaji T, et al. 2016 APL Photonics 1 060801 Google Scholar
[127]	Cirac J I, Zoller P 1995 Phys. Rev. Lett. 74 4091 Google Scholar
[128]	Wunderlich H, Wunderlich C, Singer K, Schmidt-Kaler F 2009 Phys. Rev. A 79 052324 Google Scholar
[129]	Stock R, James D F 2009 Phys. Rev. Lett. 102 170501 Google Scholar
[130]	Lanyon B P, Zwerger M, Jurcevic P, Hempel C, Dür W, Briegel H J, Blatt R, Roos C 2014 Phys. Rev. Lett. 112 100403 Google Scholar
[131]	You J, Wang X B, Tanamoto T, Nori F 2007 Phys. Rev. A 75 052319 Google Scholar
[132]	Zhang X, Gao K, Feng M 2006 Phys. Rev. A 74 024303 Google Scholar
[133]	Xue Z Y, Wang Z 2007 Phys. Rev. A 75 064303 Google Scholar
[134]	Xue Z Y, Zhang G, Dong P, Yi Y M, Cao Z L 2006 Eur. Phys. J. B 52 333 Google Scholar
[135]	Gong M, Chen M C, Zheng Y, et al. 2019 Phys. Rev. Lett. 122 110501 Google Scholar
[136]	Mooney G J, Hill C D, Hollenberg L C 2019 Sci. Rep. 9 13465 Google Scholar
[137]	Albarrán-Arriagada F, Barrios G A, Sanz M, et al. 2018 Phys. Rev. A 97 032320 Google Scholar
[138]	Vaucher B, Nunnenkamp A, Jaksch D 2008 New J. Phys. 10 023005 Google Scholar
[139]	Mamaev M, Blatt R, Ye J, Rey A M 2019 Phys. Rev. Lett. 122 160402 Google Scholar
[140]	Economou S E, Lindner N, Rudolph T 2010 Phys. Rev. Lett. 105 093601 Google Scholar
[141]	Gimeno-Segovia M, Rudolph T, Economou S E 2019 Phys. Rev. Lett. 123 070501 Google Scholar
[142]	Ju C, Zhu J, Peng X, Chong B, Zhou X, Du J 2010 Phys. Rev. A 81 012322 Google Scholar
[143]	Blythe P, Varcoe B 2006 New J. Phys. 8 231 Google Scholar
[144]	Takeuchi Y, Morimae T, Hayashi M 2019 Sci. Rep. 9 13585 Google Scholar
[145]	Gachechiladze M, Gühne O, Miyake A 2019 Phys. Rev. A 99 052304 Google Scholar
[146]	Mansfield S, Kashefi E 2018 Phys. Rev. Lett. 121 230401 Google Scholar
[147]	Frembs M, Roberts S, Bartlett S D 2018 New J. Phys. 20 103011 Google Scholar
[148]	Hu F, Lamata L, Wang C, Chen X, Solano E, Sanz M 2020 Phys. Rev. Appl. 13 054062 Google Scholar
[149]	Yan S, Qi H, Cui W 2020 Phys. Rev. A 102 052421 Google Scholar
[150]	Devakul T, Williamson D J 2018 Phys. Rev. A 98 022332 Google Scholar
[151]	Wei T C, Affleck I, Raussendorf R 2011 Phys. Rev. Lett. 106 070501 Google Scholar

[1]	胡飞飞, 李思莹, 朱顺, 黄昱, 林旭斌, 张思拓, 范云茹, 周强, 刘云. 用于量子纠缠密钥的多波长对量子关联光子对产生. 物理学报, 2024, 73(23): 230304. doi: 10.7498/aps.73.20241274
[2]	白健男, 韩嵩, 陈建弟, 韩海燕, 严冬. 超级里德伯原子间的稳态关联集体激发与量子纠缠. 物理学报, 2023, 72(12): 124202. doi: 10.7498/aps.72.20222030
[3]	王美红, 郝树宏, 秦忠忠, 苏晓龙. 连续变量量子计算和量子纠错研究进展. 物理学报, 2022, 71(16): 160305. doi: 10.7498/aps.71.20220635
[4]	王晨旭, 贺冉, 李睿睿, 陈炎, 房鼎, 崔金明, 黄运锋, 李传锋, 郭光灿. 量子计算与量子模拟中离子阱结构研究进展. 物理学报, 2022, 71(13): 133701. doi: 10.7498/aps.71.20220224
[5]	周宗权. 量子存储式量子计算机与无噪声光子回波. 物理学报, 2022, 71(7): 070305. doi: 10.7498/aps.71.20212245
[6]	王宁, 王保传, 郭国平. 硅基半导体量子计算研究进展. 物理学报, 2022, 71(23): 230301. doi: 10.7498/aps.71.20221900
[7]	姜达, 余东洋, 郑沾, 曹晓超, 林强, 刘伍明. 面向量子计算的拓扑超导体材料、物理和器件研究. 物理学报, 2022, 71(16): 160302. doi: 10.7498/aps.71.20220596
[8]	张结印, 高飞, 张建军. 硅和锗量子计算材料研究进展. 物理学报, 2021, 70(21): 217802. doi: 10.7498/aps.70.20211492
[9]	陈爱民, 刘东昌, 段佳, 王洪雷, 相春环, 苏耀恒. 含有Dzyaloshinskii-Moriya相互作用的自旋1键交替海森伯模型的量子相变和拓扑序标度. 物理学报, 2020, 69(9): 090302. doi: 10.7498/aps.69.20191773
[10]	何映萍, 洪健松, 刘雄军. 马约拉纳零能模的非阿贝尔统计及其在拓扑量子计算的应用. 物理学报, 2020, 69(11): 110302. doi: 10.7498/aps.69.20200812
[11]	范桁. 量子计算与量子模拟. 物理学报, 2018, 67(12): 120301. doi: 10.7498/aps.67.20180710
[12]	杨阳, 王安民, 曹连振, 赵加强, 逯怀新. 与XY双自旋链耦合的双量子比特系统的关联性与相干性. 物理学报, 2018, 67(15): 150302. doi: 10.7498/aps.67.20180812
[13]	秦猛, 李延标, 白忠. 非均匀磁场和杂质磁场对自旋1系统量子关联的影响. 物理学报, 2015, 64(3): 030301. doi: 10.7498/aps.64.030301
[14]	谢美秋, 郭斌. 不同磁场环境下Heisenberg XXZ自旋链中的热量子失协. 物理学报, 2013, 62(11): 110303. doi: 10.7498/aps.62.110303
[15]	樊开明, 张国锋. 阻尼Jaynes-Cummings模型中两原子的量子关联动力学. 物理学报, 2013, 62(13): 130301. doi: 10.7498/aps.62.130301
[16]	杨阳, 王安民. 与Ising链耦合的中心双量子比特系统的量子关联. 物理学报, 2013, 62(13): 130305. doi: 10.7498/aps.62.130305
[17]	赵建辉, 王海涛. 应用多尺度纠缠重整化算法研究量子自旋系统的量子相变和基态纠缠. 物理学报, 2012, 61(21): 210502. doi: 10.7498/aps.61.210502
[18]	周南润, 曾宾阳, 王立军, 龚黎华. 基于纠缠的选择自动重传量子同步通信协议. 物理学报, 2010, 59(4): 2193-2199. doi: 10.7498/aps.59.2193
[19]	叶宾, 须文波, 顾斌杰. 量子Harper模型的量子计算鲁棒性与耗散退相干. 物理学报, 2008, 57(2): 689-695. doi: 10.7498/aps.57.689
[20]	叶宾, 谷瑞军, 须文波. 周期驱动的Harper模型的量子计算鲁棒性与量子混沌. 物理学报, 2007, 56(7): 3709-3718. doi: 10.7498/aps.56.3709

计量

文章访问数: 9932
PDF下载量: 740
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

基于测量的量子计算研究进展