  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.
