Nested Quantum Walks with Quantum Data Structures [chapter]

Stacey Jeffery, Robin Kothari, Frederic Magniez
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
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
more » ... it 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.
doi:10.1137/1.9781611973105.106 dblp:conf/soda/JefferyKM13 fatcat:3lhu2elwmbhspkcszgicjgxzmi