ua nt - p h / 01 07 01 2 v 1 3 J ul 2 00 1 Quantum neural network

It is suggested that a quantum neural network (QNN), a type of artificial neural network, can be built using the principles of quantum information processing. The input and output qubits in the QNN can be implemented by optical modes with different polarization, the weights of the QNN can be implemented by optical beam splitters and phase shifters. Since it was first proposed by Feynman [1], that quantum mechanics might be more powerful computationally than a classical Turing machine, we have heard a lot of quantum computational networks [3], quantum cellular au-tomata [2], but not about quantum neural networks. The possible reason for the omni-penetrating ideas of quantum information processing (QIP) to avoid the field of artificial neural networks (ANN), is the presence of a non-linear activation function in any ANN. For very similar reason, a need for nonlinear couplings between optical modes was the main obstacle for building a scalable optical QIP system. It was shown recently [4], that quantum computation on optical modes using only beam splitters, phase shifters, photon sources and photo detectors is possible. Accepting the ideas of [4], we just assume the existence of a qubit |x = α|0 + β|1, (1) where |α| 2 + |β| 2 = 1, with the states |0 and |1 are understood as different polarization states of light. Let us consider a perceptron, i.e. the system with n input channels x 1 ,. .. , x n and one output channel y. The output of a classical perceptron [5] is y = f (n j=1 w j x j), (2)