close this message
arXiv smileybones

arXiv Is Hiring a DevOps Engineer

Advertisement

Work on one of the world's most important websites and make an impact on open science.

View Jobs
Skip to main content
Cornell University
Advertisement

arXiv Is Hiring a DevOps Engineer

View Jobs
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arxiv logo > quant-ph > arXiv:1105.4024

Help | Advanced Search

arXiv logo
Cornell University Logo

quick links

  • Login
  • Help Pages
  • About

Quantum Physics

arXiv:1105.4024 (quant-ph)
[Submitted on 20 May 2011]

Title:Span Programs for Functions with Constant-Sized 1-certificates

Authors:Aleksandrs Belovs
View a PDF of the paper titled Span Programs for Functions with Constant-Sized 1-certificates, by Aleksandrs Belovs
View PDF
Abstract:Besides the Hidden Subgroup Problem, the second large class of quantum speed-ups is for functions with constant-sized 1-certificates. This includes the OR function, solvable by the Grover algorithm, the distinctness, the triangle and other problems. The usual way to solve them is by quantum walk on the Johnson graph.
We propose a solution for the same problems using span programs. The span program is a computational model equivalent to the quantum query algorithm in its strength, and yet very different in its outfit.
We prove the power of our approach by designing a quantum algorithm for the triangle problem with query complexity $O(n^{35/27})$ that is better than $O(n^{13/10})$ of the best previously known algorithm by Magniez et al.
Comments: 15 pages, 1 figure
Subjects: Quantum Physics (quant-ph)
Cite as: arXiv:1105.4024 [quant-ph]
  (or arXiv:1105.4024v1 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.1105.4024
arXiv-issued DOI via DataCite

Submission history

From: Aleksandrs Belovs [view email]
[v1] Fri, 20 May 2011 07:12:35 UTC (25 KB)
Full-text links:

Access Paper:

    View a PDF of the paper titled Span Programs for Functions with Constant-Sized 1-certificates, by Aleksandrs Belovs
  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
quant-ph
< prev   |   next >
new | recent | 2011-05

References & Citations

  • INSPIRE HEP
  • NASA ADS
  • Google Scholar
  • Semantic Scholar

1 blog link

(what is this?)
a export BibTeX citation Loading...

BibTeX formatted citation

×
Data provided by:

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
  • Author
  • Venue
  • Institution
  • Topic

arXivLabs: experimental projects with community collaborators

Advertisement

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)
  • About
  • Help
  • contact arXivClick here to contact arXiv Contact
  • subscribe to arXiv mailingsClick here to subscribe Subscribe
  • Copyright
  • Privacy Policy
  • Web Accessibility Assistance
  • arXiv Operational Status
    Get status notifications via email or slack