Maxwell West, Diego García-Martín, N. L. Diaz, M. Cerezo, Martin Larocca (Jun 24 2025).
Abstract: Constructing ensembles of circuits which efficiently approximate the Haar measure over various groups is a long-standing and fundamental problem in quantum information theory. Recently it was shown that one can obtain approximate designs over the unitary group with depths scaling logarithmically in the number of qubits, but that no sublinear-depth approximate designs exist over the orthogonal group. Here we derive, for any group
G possessing an invariant state