Experimental verification of group non-membership in optical circuits

Sun, Kai1,2; Zhang, Zi-Jian3; Meng, Fei3,4; Cheng, Bin3,5; Cao, Zhu6; Xu, Jin-Shi1,2; Yung, Man-Hong3,7,8; Li, Chuan-Feng1,2; Guo, Guang-Can1,2

2021-09-01

10.1364/PRJ.427897

Photonics Research   影响因子和分区

2327-9125

The class quantum Merlin-Arthur (QMA), as the quantum analog of nondeterministic polynomial time, contains the decision problems whose YES instance can be verified efficiently with a quantum computer. The problem of deciding the group non-membership (GNM) of a group element is conjectured to be a member of QMA. Previous works on the verification of GNM, which still lacks experimental demonstration, required a quantum circuit with O(n(5)) group oracle calls. Here, we provide an efficient way to verify GNM problems, in which each quantum circuit only contains O(n(5)) group of oracle calls, and the number of qubits in each circuit is reduced by half. Based on this protocol, we then experimentally demonstrate the new verification process with a four-element group in an all-optical circuit. The new protocol is validated experimentally by observing a significant completeness-soundness gap between the probabilities of accepting elements in and outside the subgroup. This work efficiently simplifies the verification of GNM and is helpful in constructing more quantum protocols based on the near-term quantum devices. (C) 2021 Chinese Laser Press

SCI ; EI

英语

通讯

National Key Research and Development Program of China["2016YFA0302700","2017YFA0304100"] ; National Natural Science Foundation of China[11821404,11774335,61725504,61805227,61975195,"U19A2075",11875160,"U1801661"] ; Anhui Initiative in Quantum Information Technologies["AHY060300","AHY020100"] ; Key Research Program of Frontier Science, CAS[QYZDYSSWSLH003] ; Science Foundation of the CAS[ZDRW-XH-2019-1] ; Fundamental Research Funds for the Central Universities["WK2030380017","WK2030380015","WK2470000026"] ; Natural Science Foundation of Guangdong Province[2017B030308003] ; Key R&D Program of Guangdong Province[2018B030326001] ; Science, Technology and Innovation Commission of Shenzhen Municipality["JCYJ20170412152620376","JCYJ20170817105046702","KYTDPT20181011104202253"] ; Economy, Trade and Information Commission of Shenzhen Municipality[201901161512] ; Guangdong Provincial Key Laboratory[2019B121203002]

Optics

Optics

WOS:000692325600011

CHINESE LASER PRESS

20213710897607

Polynomial approximation ; Qubits ; Timing circuits

Pulse Circuits:713.4 ; Numerical Methods:921.6 ; Quantum Theory; Quantum Mechanics:931.4

Web of Science

1.Univ Sci & Technol China, CAS Key Lab Quantum Informat, Hefei 230026, Peoples R China
2.Univ Sci & Technol China, CAS Ctr Excellence Quantum Informat & Quantum Phy, Hefei 230026, Peoples R China
3.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
4.Univ Hong Kong, Dept Comp Sci, Pokfulam, Hong Kong, Peoples R China
5.Univ Technol Sydney, Fac Engn & Informat Technol, Ctr Quantum Software & Informat, Sydney, NSW 2007, Australia
6.East China Univ Sci & Technol, Minist Educ, Key Lab Adv Control & Optimizat Chem Proc, Shanghai 200237, Peoples R China
7.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
8.Southern Univ Sci & Technol, Shenzhen Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China

Sun, Kai,Zhang, Zi-Jian,Meng, Fei,et al. Experimental verification of group non-membership in optical circuits[J]. Photonics Research,2021,9(9):1745-1751.

Sun, Kai.,Zhang, Zi-Jian.,Meng, Fei.,Cheng, Bin.,Cao, Zhu.,...&Guo, Guang-Can.(2021).Experimental verification of group non-membership in optical circuits.Photonics Research,9(9),1745-1751.

Sun, Kai,et al."Experimental verification of group non-membership in optical circuits".Photonics Research 9.9(2021):1745-1751.