Meeting notes 11 05 26

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Aram and Thomas

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


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


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 <math>g_1g_2^{-1}\in H</math>. The goal is to find H.

One strategy is to create <math>\rho_H = \frac{1}{|G|} \sum_{g\in G} |gH\rangle\langle gH|</math> 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 <math>\rho_H</math> and the group is the dihedral group.

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