A Derivative-free Method for Quantum Perceptron Training in Multi-layered Neural Networks

In this paper, we present a gradient-free approach for training multi-layered neural networks based upon quantum perceptrons. Here, we depart from the classical perceptron and the elemental operations on quantum bits, i.e. qubits, so as to formulate the problem in terms of quantum perceptrons. We then make use of measurable operators to define the states of the network in a manner consistent with a Markov process. This yields a Dirac-Von Neumann formulation consistent with quantum mechanics. Moreover, the formulation presented here has the advantage of having a computational efficiency devoid of the number of layers in the network. This, paired with the natural efficiency of quantum computing, can imply a significant improvement in efficiency, particularly for deep networks. Finally, but not least, the developments here are quite general in nature since the approach presented here can also be used for quantum-inspired neural networks implemented on conventional computers.