Model and Algorithm of Neural Networks with Quantum Gated Nodes

Summary

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On the basis of analyzing the principles of the quantum, rotation gates and quantum controlled-NOT gates, an improved design for CNOT gated quantum neural networks model is proposed and a smart algorithm for it is derived in our paper, based on the gradient descent algorithm. In the improved model, the input information is expressed by the qubits, which, as the control qubits after being rotated by the rotation gate, control the qubits in the hidden layer to reverse. The qubits in the hidden layer, as the control qubits after being rotated by the rotation gate, control the qubits in the output layer to reverse. The networks output is described by the probability amplitude of state |1[right angle bracket] in the output layer. It has been shown in two application examples of pattern recognition and function approximation that the proposed model is superior to the standard error back-propagation networks with regard to their convergence rate, number of iterations, approximation ability, and robustness.

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Model and Algorithm of Neural Networks with Quantum Gated Nodes

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1. Introduction

In the 1980s, BeniofF first proposed the concept of quantum computation [I]. Shor discussed the first quantum algorithm of very large integer factorization [2] in 1994. In 1996, Grover explored an important quantum algorithm, which can search for a marked state in an unordered list [3]. Although the quantum machines are not yet technologically feasible, the quantum algorithms that can be applied on quantum computers are indeed interesting and significantly different from classical computing. As we know, fuzzy logic, evolutionary computation, and neural networks are regarded as intelligent computing (soft computing), and also have some comparability with quantum computation [4]. Therefore, combination of these computing methods is emerging. Different from Hebbian learning, a quantum neural network can be used for enriched learning of neural networks. Proposed by Penrose in 1989 [5], the idea of quantum information processing in the human brain is still a controversial theory, which has not been experimentally proved. However, the exploration of quantum information devices is a promisi...

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