Simple constructions of linear-depth t-designs and pseudorandom unitaries

arXiv:2404.12647v1 Announce Type: cross
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 …

arxiv cs.cr depth line linear measure quant-ph random research simple