Designs from magic-augmented Clifford circuits

Abstract

In this talk, I will introduce magic-augmented Clifford circuits -- architectures in which Clifford circuits are preceded and/or followed by constant-depth circuits of non-Clifford (``magic") gates -- as a resource-efficient way to realize approximate k-designs. We prove that shallow Clifford circuits, when augmented with constant-depth circuits of magic gates, can generate approximate unitary and state k-designs with bounded relative error. The total circuit depth for these constructions improves upon previous results for small k>=4. The required number of magic gates is further reduced when considering k-designs with bounded additive error. We show that shallow Clifford circuits followed by O(k^2) single-qubit magic gates can generate an additive-error state k-design. I will also provide classical statistical mechanics understanding of our results and discuss the no-go theorems on design generation.