Detecting quantum speedup of random walks with machine learning

TL;DR

This paper investigates using machine learning, specifically neural networks, to detect quantum speedup in random walks on graphs, highlighting challenges and potential for insights into quantum advantage.

Contribution

It introduces neural network approaches to identify quantum speedup in graph-based random walks and analyzes their effectiveness and limitations.

Findings

Neural networks can be trained to detect quantum speedup with proper data preparation.

Current architectures struggle with large random graphs and cross-size generalization.

Improving classification accuracy could provide new insights into quantum advantage.

Abstract

We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and convolutional neural networks) for identifying linear, cyclic, and random graphs that yield quantum speedups in terms of the hitting time for reaching a target node after starting in another node of the graph. Our results indicate that carefully building the data set for training can improve the performance of the neural networks, but all architectures we test struggle to classify large random graphs and generalize from training on one graph size to testing on another. If classification accuracy can be improved further, valuable insights about quantum advantage may be gleaned from these neural networks, not only for random walks, but more generally for quantum computing and quantum transport.