00921nas a2200109   4500000000100000000000100001008004100002100002200043700002400065245005500089520066700144                                       d1 aMarcin Markiewicz1 aKonrad Schlichtholz00aUnitary operator bases as universal averaging sets3 a<p>We provide a generalization of the idea of unitary designs to cover finite averaging over much more general operations on quantum states. Namely, we construct finite averaging sets for averaging quantum states over arbitrary reductive Lie groups, on condition that the averaging is performed uniformly over the compact component of the group. Our construction comprises probabilistic mixtures of unitary 1-designs on specific operator subspaces. Provided construction is very general, competitive in the size of the averaging set when compared to other known constructions, and can be efficiently implemented in the quantum circuit model of computation.</p>