A Simple Quantum Neural Net with a Periodic Activation Function
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In this paper, we propose a simple neural net that requires only O(nlog_2k) numbers of quantum gates and qubits: Here, n is the number of input parameters, and k is the number of weights applied to these input parameters in the proposed neural net. We describe the network in terms of a quantum circuit, and then draw its equivalent classical neural net which involves O(k^n) nodes in the hidden layer. Then, we show that the network uses a periodic activation function of cosine values of the linear combinations of the inputs and weights. The steps of the gradient descent are described, and then Iris and Breast cancer datasets are used for the numerical simulations. The numerical results indicate the network can be used in machine learning problems and it may provide exponential speedup over the same structured classical neural net.
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