Experimental verification of group non-membership in optical circuits  

作　　者：KAI SUN ZI-JIAN ZHANG FEI MENG BIN CHENG ZHU CAO JIN-SHI XU MAN-HONG YUNG CHUAN-FENG LI GUANG-CAN GUO 

机构地区：[1]CAS Key Laboratory of Quantum Information,University of Science and Technology of China,Hefei 230026,China [2]CAS Center for Excellence in Quantum Information and Quantum Physics,University of Science and Technology of China,Hefei 230026,China [3]Department of Physics,Southern University of Science and Technology,Shenzhen 518055,China [4]Department of Computer Science,The University of Hong Kong,Pokfulam,Hong Kong SAR,China [5]Centre for Quantum Software and Information,Faculty of Engineering and Information Technology,University of Technology Sydney,Sydney,NSW 2007,Australia [6]Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education,East China University of Science and Technology,Shanghai 200237,China [7]Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen 518055,China [8]Shenzhen Key Laboratory of Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen 518055,China

出　　处：《Photonics Research》2021年第9期1745-1751,共7页光子学研究（英文版）

基　　金：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)。

摘　　要：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(1)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.

关 键 词：QUANTUM ELEMENT POLYNOMIAL 

分 类 号：O413[理学—理论物理]