Statistical Complexity of Quantum Learning

Banchi, Leonardo; Pereira, Jason Luke; Jose, Sharu Theresa; Simeone, Osvaldo

doi:10.1002/qute.202300311

Title: Statistical Complexity of Quantum Learning

Journal Article · 14 April 2024 · Advanced Quantum Technologies

DOI: https://doi.org/10.1002/qute.202300311 · OSTI ID:2481134

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Department of Physics and Astronomy University of Florence, and INFN Sezione di Firenze via G. Sansone 1 Sesto Fiorentino FI I‐50019 Italy
INFN Sezione di Firenze via G. Sansone 1 Sesto Fiorentino FI I‐50019 Italy
Department of Computer Science University of Birmingham Birmingham B15 2TT UK
King's Learning and Information Processing Lab (KCLIP) Centre for Intelligent Information Processing Systems (CIIPS) Department of Engineering King's College London Strand London WC2R 2LS UK

Abstract Learning problems involve settings in which an algorithm has to make decisions based on data, and possibly side information such as expert knowledge. This study has two main goals. First, it reviews and generalizes different results on the data and model complexity of quantum learning, where the data and/or the algorithm can be quantum, focusing on information‐theoretic techniques. Second, it introduces the notion of copy complexity, which quantifies the number of copies of a quantum state required to achieve a target accuracy level. Copy complexity arises from the destructive nature of quantum measurements, which irreversibly alter the state to be processed, limiting the information that can be extracted about quantum data. As a result, empirical risk minimization is generally inapplicable. The paper presents novel results on the copy complexity for both training and testing. To make the paper self‐contained and approachable by different research communities, an extensive background material is provided on classical results from statistical learning theory, as well as on the distinguishability of quantum states. Throughout, the differences between quantum and classical learning are highlighted by addressing both supervised and unsupervised learning, and extensive pointers are provided to the literature.

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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-07CH11359

OSTI ID:: 2481134

Journal Information:: Advanced Quantum Technologies, Journal Name: Advanced Quantum Technologies; ISSN 2511-9044

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: Germany

Language:: English

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