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

Nested Quantum Walks with Quantum Data Structures

Abstract

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.

Formats available

You can view the full content in the following formats:

Information & Authors

Information

Published In

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

History

Published online: 18 December 2013

Authors

Affiliations

Notes

*
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.

Metrics & Citations

Metrics

Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited By

There are no citations for this item

View Options

View options

PDF

View PDF

Get Access

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share on social media

On May 28, 2024, our site will enter Read Only mode for a limited time in order to complete a platform upgrade. As a result, the following functions will be temporarily unavailable: registering new user accounts, any updates to existing user accounts, access token activations, and shopping cart transactions. Contact [email protected] with any questions.