How fast can quantum circuits compile group designs?Recent work arxiv.org/abs/2407.07754 showed that designs over the n-qubit unitary group can be compiled in logarithmic-in-n depth. Can we similarly build short-depth designs over other groups? In our new paper arxiv.org/abs/2506.16005 we answer no.
No-go theorems for sublinear-depth group designs
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 th...
arxiv.org