  We develop a new framework that extends the quantum walk framework of
Magniez, Nayak, Roland, and Santha, by utilizing the idea of quantum data
structures to construct an efficient method of nesting quantum walks.
Surprisingly, only classical data structures were considered before for
searching via quantum walks.
  The recently proposed learning graph framework of Belovs has yielded improved
upper bounds for several problems, including triangle finding and more general
subgraph detection. We exhibit the power of our framework by giving a simple
explicit constructions that reproduce both the $O(n^{35/27})$ and $O(n^{9/7})$
learning graph upper bounds (up to logarithmic factors) for triangle finding,
and discuss how other known upper bounds in the original learning graph
framework can be converted to algorithms in our framework. We hope that the
ease of use of this framework will lead to the discovery of new upper bounds.
