# Meeting notes 11 05 26

Aram and Thomas

We thought about classical exponential de Finetti. The straightforward analogue doesn't work. Maybe something else does.

Kamil

Non-trivial non-universal QCAs? Consider the kind that look like tensor products of single-qubit gates, conjugated by a big unitary.

Bacon

The hidden subgroup problem: f is a function from a group G to a set S, which has the promise that for some subgroup H of G, f(g1)=f(g2) iff $g_1g_2^{-1}\in H$. The goal is to find H.

One strategy is to create $\rho_H = \frac{1}{|G|} \sum_{g\in G} |gH\rangle\langle gH|$ and to do optimal estimation of H, or at least the pretty-good measurement. See work of Bacon, Childs, van Dam for case when we take many copies of $\rho_H$ and the group is the dihedral group.

Idea: Replace G with $\bar G = G \rtimes \tilde G$, and f with $\bar f:\bar G\rightarrow S$. In some cases, this can increase the probability of success when you restrict to projective measurements.