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arXiv:2309.02212

Detecting quantum speedup of random walks with machine learning

Hanna Linn, Yu Zheng, Anton Frisk Kockum

Published Sep 5, 2023• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2309.02212

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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.
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We study hitting times of quantum walks on graphs from a machine learning perspective. Given a graph it is difficult to decide if quantum walks give an advantage relative to classical random walks. It was shown that machine learning can help to detect quantum advantage even though quantum walk and random walk dynamics on the graph has never been simulated. Here we describe the procedure by which training data is generated for the machine learning approach, and discuss possible future improvements.
The development of Graph Neural Networks (GNNs) has led to great progress in machine learning on graph-structured data. These networks operate via diffusing information across the graph nodes while capturing the structure of the graph. Recently there has also seen tremendous progress in quantum computing techniques. In this work, we explore applications of multi-particle quantum walks on diffusing information across graphs. Our model is based on learning the operators that govern the dynamics of quantum random walkers on graphs. We demonstrate the effectiveness of our method on classification and regression tasks.
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Abstract Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here, it is shown that the process of finding these requirements can be automated by learning from simulated examples. The automation is done by using a convolutional neural network of a particular type that learns to understand with which network and under which coherence requirements quantum advantage is possible. The machine learning approach is applied to study noisy quantum walks on cycle graphs of different sizes. It is found that it is possible to predict the existence of quantum advantage for the entire decoherence parameter range, even for graphs outside of the training set. The results are of importance for demonstration of advantage in quantum experiments and pave the way toward automating scientific research and discoveries.