Universal algorithms for quantum data learning

Fanizza, Marco; Skotiniotis, Michael; Calsamiglia, John; Muñoz-Tapia, R.; Sentís, Gael

doi:10.1209/0295-5075/ac9c29

EPL

2022

DOI: 10.1209/0295-5075/ac9c29

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Universal algorithms for quantum data learning

Marco Fanizza

Michael Skotiniotis

John Calsamiglia

et al.

Abstract: Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this Perspective, we review a line of works dealing with measurements that reveal structural properties of quantum datasets given in the form of product states. These algorithms are universal, meaning that their performances do not depend on the reference frame in which the dataset is pr… Show more

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2024

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Cited by 3 publications

References 47 publications

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Statistical Complexity of Quantum Learning

Banchi,

Pereira,

Jose

et al. 2024

Adv Quantum Tech

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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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Statistical Complexity of Quantum Learning

Banchi,

Pereira,

Jose

et al. 2024

Adv Quantum Tech

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XpookyNet: advancement in quantum system analysis through convolutional neural networks for detection of entanglement

Kookani,

Mafi,

Kazemikhah

et al. 2024

Quantum Mach. Intell.

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Quantum multi-anomaly detection

Llorens,

Sentís,

Muñoz-Tapia

2024

Quantum

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A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of n preparations with k anomalies. We analyze the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory, thus establishing a connection between graph theory and quantum hypothesis testing. In particular, we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large n and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires a universal protocol for which we prove that in the asymptotic limit, the success probability corresponds to the average of the known state scenario.

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Universal algorithms for quantum data learning

Cited by 3 publications

References 47 publications

Statistical Complexity of Quantum Learning

Statistical Complexity of Quantum Learning

XpookyNet: advancement in quantum system analysis through convolutional neural networks for detection of entanglement

Quantum multi-anomaly detection

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