Universal algorithms for quantum data learning
Marco Fanizza, Michalis Skotiniotis, John Calsamiglia, Ramon, Mu\~noz-Tapia, and Gael Sent\'is
TL;DR
This paper reviews universal quantum algorithms for learning from quantum data, focusing on measurements that reveal structural properties of datasets in the form of product states, independent of reference frames.
Contribution
It introduces a framework for universal measurements in quantum data learning, characterized through group representation theory, applicable regardless of reference frame.
Findings
Universal algorithms do not depend on reference frames.
Optimal measurements are characterized via group representation theory.
The approach applies to datasets of product states.
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 provided. Requiring the universality property implies a characterization of optimal measurements via group representation theory.
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