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Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms

Nested Quantum Walks with Quantum Data Structures


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(n35/27) and O(n9/7) 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.

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cover image Proceedings
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
Pages: 1474 - 1485
Editor: Sanjeev Khanna, University of Pennsylvania, Philadelphia, Pennsylvania
ISBN (Print): 978-1-611972-51-1
ISBN (Online): 978-1-61197-310-5


Published online: 18 December 2013




Partially supported by the French ANR Defis project ANR-08-EMER-012 (QRAC), the European Commission IST STREP project 25596 (QCS), NSERC, NSERC Frequency, MITACS, and the Ontario Ministry of Research and Innovation.

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