Efficient Constructions of Linear-Depth Unitary t-Designs and Pseudorandom Unitaries

The authors introduce the "PFC ensemble" - the product of a random computational basis permutation, a random binary phase operator, and a random Clifford unitary - and show that it approximates the Haar measure up to exponentially high moments. They then derandomize this ensemble to construct the first linear-depth t-designs and the first non-adaptive pseudorandom unitaries.