Abstract
Approximate t-design are ensembles of unitaries that (approximately) recover Haar averages of polynomials in entries of unitaries up to the order t. As such, they find numerous applications throughout quantum information, including randomized benchmarking , efficient estimation of properties of quantum states, decoupling, information transmission and quantum state discrimination. In this talk I will characterize how finite random gate-sets mimic the Haar measure.
The talk will be based on the joint word with Piotr Dulian.
arXiv:2210.07872
