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

TL;DR

This paper introduces a gradient-free quantum perceptron training method for multi-layered neural networks, leveraging quantum mechanics principles to improve efficiency and applicability to quantum-inspired classical neural networks.

Contribution

It proposes a novel quantum perceptron-based training approach that is gradient-free, layer-independent in computational complexity, and applicable to quantum-inspired neural networks.

Findings

Potential for significant efficiency improvements in deep networks

Formulation consistent with quantum mechanics and Markov processes

Applicable to both quantum and classical quantum-inspired neural networks

Abstract

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.