Introduction to Quantum Singular Value Transform with applications to Petz map, Polar decomposition and Pretty-Good Measurements

Abstract: The recently-introduced quantum algorithmic technique of quantum singular value transform (QSVT) has been hailed as a `grand unification of quantum algorithms’.

In this talk, we give a pedagogical introduction to this toolbox, and illustrate its flexibility and precision by using it to implement tools in quantum linear algebra, quantum noise recovery and optimal quantum measurements: i) the quantum polar decomposition ii) the Petz recovery channel iii) pretty-good measurements. Previously, a significant hurdle to the experimental realization of these vaunted theoretical tools was the lack of a systematic and efficient method to implement them; we rectify this lack by proposing quantum algorithms for all three tools based on QSVT.

This talk is based on arXiv:2006.16924 and arXiv:2106.07634.

quantum computing and information

Audience: researchers in the topic

( paper )

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SEMINAR HOSTED BY: Dr Mária Kieferová, Centre for Quantum Software and Information, University of Technology Sydney, Australia

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Centre for Quantum Software and Information Seminar Series

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