Designs from magic-augmented Clifford circuits

Yimu Bao shows how shallow Clifford circuits augmented by constant-depth non-Clifford gates can produce approximate unitary and state k-designs. The construction improves depth requirements for small k of at least four. For bounded additive error, a shallow Clifford circuit followed by O(k²) single-qubit magic gates suffices for a state design. The talk interprets these results using classical statistical mechanics and discusses limitations imposed by no-go theorems.