Implementation of quantum stochastic walks for function approximation, two-dimensional data classification, and sequence classification

TL;DR

This paper demonstrates that quantum stochastic walks can be used to implement neural networks capable of function approximation and data classification, showing advantages in accuracy and robustness over classical and decoherent models.

Contribution

It introduces a quantum stochastic neural network model based on quantum walks, demonstrating its effectiveness in various classification tasks and its robustness against noise.

Findings

QSNN reduces training steps in sequence classification

Quantum advantage in recognizing new input types

Coherent QSNN is more robust against noise

Abstract

We study a quantum stochastic neural network (QSNN) based on quantum stochastic walks on a graph, and use gradient descent to update the network parameters. We apply a toy model of QSNN with a few neurons to the problems of function approximation, two-dimensional data classification, and sequence classification. A simple QSNN with five neurons is trained to determine whether a sequence of words is a sentence or not, and we find that a QSNN can reduce the number of training steps. A QSNN with 11 neurons shows a quantum advantage in improving the accuracy of recognizing new types of inputs like verses. Moreover, with our toy model, we find the coherent QSNN is more robust against both label noise and device noise, compared with the decoherent QSNN. These results show that quantum stochastic walks may be a useful resource to implement a quantum neural network.