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تسجيل مستخدم جديدQuantum Walk to Train a Classical Artificial Neural Network
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This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to simulate a quantum machine to execute the quantum walk. In this way, to minimize the computational cost, the methodology employed to train the neural network will adjust the synaptic weights of the output layer, not altering the weights of the hidden layer, inspired in the method of Extreme Learning Machine. The quantum walk algorithm as a search algorithm is quadratically faster than its classic analog. The quantum walk variance is $O(t)$ while the variance of its classic analog is $O(sqrt{t})$, where $t$ is the time or iteration. In addition to computational gain, another advantage of the proposed procedure is to be possible to know textit{a priori} the number of iterations required to obtain the solutions, unlike the classical training algorithms based on gradient descendent.
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This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic weights of
a classical artificial neural network. Each vertex of this complete graph represents a possible synaptic weight set in the $w$-dimensional search space, where $w$ is the number of weights of the neural network. To know the number of iterations required textit{a priori} to obtain the solutions is one of the main advantages of the procedure. Another advantage is that the proposed method does not stagnate in local minimums. Thus, it is possible to use the quantum walk search procedure as an alternative to the backpropagation algorithm. The proposed method was employed for a $XOR$ problem to prove the proposed concept. To solve this problem, the proposed method trained a classical artificial neural network with nine weights. However, the procedure can find solutions for any number of dimensions. The results achieved demonstrate the viability of the proposal, contributing to machine learning and quantum computing researches.
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