一种酉权重量子感知机
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摘要
通过将量子计算与经典感知机网络相结合,提出了一种基于酉权重的新型高效量子感知机算法.在算法过程中通过求解总的权重矩阵,并对其进行奇异值分解来保持其具有酉性.与其他人提出的量子感知机算法不同,本算法在非理想训练算例(超完备和欠完备)条件下,通过一次迭代训练学习可实现Hadamard门H、相位门S、受控非门CNOT、π/8门T这些基本量子门功能,这些基本量子门是构成任意量子门的标准集合,因此理论上该算法也能够实现任意量子门功能.最后,通过选择一个由多个基本量子门构成的组合门作为实例,以及随机选取一个训练集对算法的通用性进行了进一步验证.
By combining quantum computing with classical perceptron network,a novel and efficient algorithm,called quantum perceptron algorithm,based on the unitary weights is proposed. In order to make the weight matrix to be unitary,the total weight matrix is firstly computed,and then the singular value decomposition is utilized. Different from the previous quantum perceptron algorithms,the present algorithm can realize basic quantum gate functions: Hadamard gate,phase gate,controlled-not(CNOT) gate,and π/8 gate,which can be realized by one iteration training in the imperfect training case(such as,over-complete,less-complete). These basic quantum gates are the standard set of arbitrary quantum gates,so theoretically the algorithm can also realize any quantum gate function.Finally,the generality of the algorithm is further verified by selecting a composite gate composed of multiple basic quantum gates as an example and randomly selected a training set.
By combining quantum computing with classical perceptron network,a novel and efficient algorithm,called quantum perceptron algorithm,based on the unitary weights is proposed. In order to make the weight matrix to be unitary,the total weight matrix is firstly computed,and then the singular value decomposition is utilized. Different from the previous quantum perceptron algorithms,the present algorithm can realize basic quantum gate functions: Hadamard gate,phase gate,controlled-not(CNOT) gate,and π/8 gate,which can be realized by one iteration training in the imperfect training case(such as,over-complete,less-complete). These basic quantum gates are the standard set of arbitrary quantum gates,so theoretically the algorithm can also realize any quantum gate function.Finally,the generality of the algorithm is further verified by selecting a composite gate composed of multiple basic quantum gates as an example and randomly selected a training set.
引文
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[8]Zhou Ri-gui.Research on quantum neural network model[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2008.
[9]Sagheer A,Zidan M.Autonomous quantum perceptron neural netw ork[J].Physics Chemical Research in Chinese Universities,2013,66(11):1813-1818.
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[8]周日贵.量子神经网络模型研究[D].南京:南京航空航天大学,2008.
[2]Feynman R P.Simulating physics with computers[J].International Journal of Theoretical Physics,1982,21(6):467-488.
[3]Shor P W.Algorithms for quantum computation:discrete logarithms and factoring[C].Proceedings 35th Annual Symposium on Foundations of Computer Science,New mexico,USA:IEEE Conference Publications,1994.
[4]Shor P W.Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer[J].Siam Review,1997,41(2):1484-1509.
[5]Grover L K.Quantum mechanics helps in searching for a needle in a haystack[J].Physical Review Letters,1997,79(2):325-328.
[6]Schuld M,Sinayskiy I,Petruccione F.The quest for a quantum neural netw ork[J].Quantum Information Processing,2014,13(11):2567-2586.
[7]Altaisky M V.Quantum neural network[J].International Journal of Theoretical Physics,2001,36(12):2855-2875.
[8]Zhou Ri-gui.Research on quantum neural network model[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2008.
[9]Sagheer A,Zidan M.Autonomous quantum perceptron neural netw ork[J].Physics Chemical Research in Chinese Universities,2013,66(11):1813-1818.
[10]Siomau M.A quantum model for autonomous learning automata[J].Quantum Information Processing,2014,13(2):1211-1221.
[11]Seow K L,Behrman E,Steck J.Efficient learning algorithm for quantum perceptron unitary w eights[J].Ar Xiv Preprint,2015,1512(00522):1-10.
[12]Rosenblatt F.The perceptron:a probabilistic model for information storage and organization in the brain[J].Psychological Review,1958,65(6):386-408.
[13]Nielsen M A,Chuang I L.Quantum computation and quantum information[M].Cambridgeshire,UK:Cambridge University Press,2000.
[8]周日贵.量子神经网络模型研究[D].南京:南京航空航天大学,2008.