Quantum neural networks model based on swap test and phase estimation

In this paper, a neural networks model for quantum computer is proposed. The core of this model is quantum neuron. Firstly, the inner product of the input qubits and the weight qubits is mapped to the phase of the control qubits in the neuron by the swap test technology, and then these phases are obtained by the phase estimation method, which are further used as the phase of the output qubit in the neuron. In this way, the mapping of input qubits to output qubit in quantum neuron is completed. The quantum neurons mentioned above can be used to construct quantum neural networks. In this paper, the quantum circuit for each operation step are given. The simulation results on the classic computer verify the effectiveness of the proposed model.

[1]  Yunpeng Ma,et al.  Research and application of quantum-inspired double parallel feed-forward neural network , 2017, Knowl. Based Syst..

[2]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[3]  Teresa Bernarda Ludermir,et al.  Quantum perceptron over a field and neural network architecture selection in a quantum computer , 2016, Neural Networks.

[4]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[5]  Morteza Tofighi,et al.  Fuzzy wavelet plus a quantum neural network as a design base for power system stability enhancement , 2015, Neural Networks.

[6]  Fariel Shafee,et al.  Neural networks with quantum gated nodes , 2002, Eng. Appl. Artif. Intell..

[7]  G. Guo,et al.  Building quantum neural networks based on a swap test , 2019, Physical Review A.

[8]  Wolfgang Porod,et al.  Quantum cellular neural networks , 1996, cond-mat/0005038.

[9]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[10]  Cheng-Jian Lin,et al.  An entropy-based quantum neuro-fuzzy inference system for classification applications , 2007, Neurocomputing.

[11]  Teresa Bernarda Ludermir,et al.  Chaos in Quantum Weightless Neuron Node Dynamics , 2016, Neurocomputing.

[12]  Sanjay Gupta,et al.  Quantum Neural Networks , 2001, J. Comput. Syst. Sci..

[13]  Tony R. Martinez,et al.  Quantum associative memory , 2000, Inf. Sci..

[14]  Ching-Ter Chang,et al.  Single-hidden-layer feed-forward quantum neural network based on Grover learning , 2013, Neural Networks.

[15]  Changpeng Shao,et al.  A quantum model of feed-forward neural networks with unitary learning algorithms , 2020, Quantum Information Processing.

[16]  Junyou Shi,et al.  Complex Rotation Quantum Dynamic Neural Networks (CRQDNN) using Complex Quantum Neuron (CQN): Applications to time series prediction , 2015, Neural Networks.

[17]  Kenli Li,et al.  The convergence and termination criterion of quantum-inspired evolutionary neural networks , 2017, Neurocomputing.

[18]  R. Cleve,et al.  Quantum fingerprinting. , 2001, Physical review letters.

[19]  R. Feynman.  Simulating physics with computers , 1999 .

[20]  S. Chakraverty,et al.  Quantum neural network based machine translator for English to Hindi , 2016, Appl. Soft Comput..

[21]  Subhash C. Kak,et al.  On Quantum Neural Computing , 1995, Inf. Sci..

[22]  Siddhartha Bhattacharyya,et al.  Binary image denoising using a quantum multilayer self organizing neural network , 2014, Appl. Soft Comput..

[23]  Kazuhiko Takahashi,et al.  Multi-layer quantum neural network controller trained by real-coded genetic algorithm , 2014, Neurocomputing.

[24]  Ajit Narayanan,et al.  Quantum artificial neural network architectures and components , 2000, Inf. Sci..

[25]  Teresa Bernarda Ludermir,et al.  Weightless neural network parameters and architecture selection in a quantum computer , 2016, Neurocomputing.

[26]  Yang Li,et al.  Quantum Algorithm Design: Techniques and Applications , 2019, J. Syst. Sci. Complex..

[27]  Xin Yin,et al.  Analog fault diagnosis using S-transform preprocessor and a QNN classifier , 2013 .

[28]  Maria Schuld,et al.  Simulating a perceptron on a quantum computer , 2014, ArXiv.

[29]  Snehashish Chakraverty,et al.  Recent Developments and Applications in Quantum Neural Network: A Review , 2018, Archives of Computational Methods in Engineering.

[30]  Cunbao Ma,et al.  Deep quantum inspired neural network with application to aircraft fuel system fault diagnosis , 2017, Neurocomputing.

[31]  Michiharu Maeda,et al.  Qubit neuron according to quantum circuit for XOR problem , 2007, Appl. Math. Comput..

[32]  Xin Li,et al.  A hybrid quantum-inspired neural networks with sequence inputs , 2013, Neurocomputing.

[33]  CuiYiqian,et al.  Complex Rotation Quantum Dynamic Neural Networks (CRQDNN) using Complex Quantum Neuron (CQN) , 2015 .

[34]  Teresa Bernarda Ludermir,et al.  Classical and superposed learning for quantum weightless neural networks , 2012, Neurocomputing.

[35]  Cunbao Ma,et al.  IMA health state evaluation using deep feature learning with quantum neural network , 2018, Eng. Appl. Artif. Intell..

[36]  Herbert Wiklicky,et al.  Tunable Quantum Neural Networks for Boolean Functions , 2020 .