Building quantum neural networks based on swap test

TL;DR

This paper introduces a quantum neural network model utilizing quantum states for neurons, inner products, and activation functions, implemented via quantum circuits, with a proposed learning algorithm and numerical validation.

Contribution

It presents a novel quantum neural network framework with quantum-based weights and operations, including a new learning algorithm and circuit implementation.

Findings

The quantum neural network model is theoretically valid.

Numerical simulations demonstrate its potential.

Quantum circuit implementation is feasible.

Abstract

Artificial neural network, consisting of many neurons in different layers, is an important method to simulate humain brain. Usually, one neuron has two operations: one is linear, the other is nonlinear. The linear operation is inner product and the nonlinear operation is represented by an activation function. In this work, we introduce a kind of quantum neuron whose inputs and outputs are quantum states. The inner product and activation operator of the quantum neurons can be realized by quantum circuits. Based on the quantum neuron, we propose a model of quantum neural network in which the weights between neurons are all quantum states. We also construct a quantum circuit to realize this quantum neural network model. A learning algorithm is proposed meanwhile. We show the validity of learning algorithm theoretically and demonstrate the potential of the quantum neural network numerically.