[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-290748-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-290748-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","detecting-quantum-speedup-of-random-walks-with-machine-learning","Detecting quantum speedup of random walks with machine learning","","We explore how machine-learning techniques can detect quantum speedup in random walks on graphs. Three neural-network architectures are trained to identify whether different graph types yield quantum advantages measured via hitting time to reach a target node from another node. Results show that better training data construction improves performance, yet all tested models struggle with large random graphs and with generalizing across graph sizes. Improved accuracy could reveal insights into quantum advantage for random walks and broader quantum technologies.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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machine learning  \nHanna Linn, 1, ∗ Yu Zheng, 1,† and Anton Frisk Kockum 1,‡  \n1 Department of Microtechnology and Nanoscience,  \nChalmers University of Technology, 412 96 Gothenburg, Sweden  \n(Dated: September 6, 2023)  \nWe 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.  \nI. INTRODUCTION  \nComputations using quantum systems [1] have the potential to offer significant speedup over classical computers for certain problems [2–9] . Indeed, some recent experiments with quantum-computing devices have challenged the limits and performances of classical computing hardware [10–15] . However, it can be difficult to find out whether a quantum computer can provide a meaningful speedup for solving a certain problem [16–20] . In many cases, it also remains an open question what quantum resources and properties of a quantum-computing device are necessary to enable a quantum advantage [1, 21–28] . In this article, we focus on quantum versions of random walks [29–36] and how to determine when they can provide an advantage over classical random walks. The classical random walk [37, 38] has many applications [35, 39– 44], both in algorithms and in modelling of physical systems. This motivated studies of quantum walks [45–50], which have turned out to be able to outperform classical random walks in some instances (usually, by traversing a graph faster) . It has also been shown that quantum walks can perform universal quantum computation [51, 52] .  \nAs such, improving the understanding of when quantum walks outperform classical random walks may give clues about when quantum computers can outperform classical computers. Recent experiments have demonstrated implementations of quantum walks on tens, hundreds, and even thousands of nodes using several hardware platforms [53–57] .  \nDetermining when quantum walks are faster than classical random walks can be done analytically or by simulating both walks on a graph. While there are analytical results for certain types of graphs [45, 58–65](and progress toward more generally applicable crite-  \n∗ Equal author contributions; [hannlinn@chalmers.se](hannlinn@chalmers.se)[ ](hannlinn@chalmers.se)† Equal author contributions; [zhyu@chalmers.se](zhyu@chalmers.se)[ ](zhyu@chalmers.se)‡ [anton.frisk.kockum@chalmers.se](anton.frisk.kockum@chalmers.se)  \nria [50, 66]), the space of possible graphs is vast. Simulations can handle any type of graphs, but only provide answers for individual cases without giving information about general properties. As the graph size and connectivity grow, the simulation time also grows; the propagation time for the walker usually scales polynomially with the size of the graph [67, 68] .  \nHere, we instead apply machine-learning methods to classify on which graphs a quantum walker will reach its target faster than a classical walker. Machine learning has in the past few years been applied to aid quantum technologies in many ways [69], e.g., for quantum error correction [70–72], quantum state and process tomography [73–77], qu","cbCaiaoJu9cm3gxs","https://ap.wps.com/l/cbCaiaoJu9cm3gxs","pdf",12128878,15,"English","# Introduction\n## Quantum versions of random walks\n## Need for detecting quantum advantage\n## Machine learning for quantum technologies","[{\"question\":\"What problem does the study address?\",\"answer\":\"The study investigates how to detect when quantum random walks outperform classical random walks, using machine-learning classification based on hitting time to a target node.\"},{\"question\":\"How do the authors evaluate quantum advantage?\",\"answer\":\"Quantum advantage is expressed in terms of hitting time: the time for a quantum walker to reach a target node from a given starting node compared against a classical walker.\"},{\"question\":\"What are the main findings about the neural networks?\",\"answer\":\"Carefully constructed training datasets improve classification performance, but all tested architectures have difficulty classifying large random graphs and generalizing from one graph size to another.\"}]","Detecting quantum speedup of random walks with machine learning | PDF",38]