Аннотация:Programmable interferometers are a key tool for realizing arbitrary unitary matrices on a linearoptical platform, a promising physical realization of quantum computing. Constructing arbitrary Haar unitary matrices requires O(N^2) programmable phase shifters, which is a computationally and experimentally challenging task. However, many applications only require reproducing the first few moments of the Haar measure, leading to the use of unitary t-designs. In this work, we present a compact interferometer scheme that efficiently generates a 1-design using only O(N) parameters, and
propose a general method for constructing t-designs of higher orders.