Adam Sawicki

A random matrix model for random approximate t-designs

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 or quantum state discrimination. In this talk I will define t-designs and review their basic properties stating some of the open problems. Then I will characterize how good t-designs are finite Haar random gate-sets. This is a joint work with Piotr Dulian (arXiv:2210.07872).

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/e126aeffbf85443e88ea14d7f1580ff51d