Tony Metger - How to derandomise the Haar measure

How to derandomise the Haar measure

This seminar, given by Tony Metger, will happend on 28 August 2024, at 12:0. It will take place in Room 25-26 105..

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Abstract

Uniformly random unitaries, i.e. unitaries drawn from the Haar measure, have many useful properties, but cannot be implemented efficiently. This has motivated a long line of research into random unitaries that look sufficiently Haar random while also being efficient to implement. Two different notions of derandomisation have emerged: t-designs are random unitaries that information-theoretically reproduce the first t moments of the Haar measure, and pseudorandom unitaries (PRUs) are random unitaries that are computationally indistinguishable from Haar random. I will explain a simple unified construction of both t-designs and PRUs from the PFC ensemble, the concatenation of a random Clifford unitary, a random binary phase, and a random computational basis state permutation. Joint work with Alexander Poremba, Makrand Sinha, and Henry Yuen (arXiv:2404.12647).