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Trapped Ion Quantum Computing

Span Programs for Functions with Constant-Sized 1-certificates

arXiv
Authors: Aleksandrs Belovs

Year

2011

Paper ID

8740

Status

Preprint

Abstract Read

~2 min

Abstract Words

120

Citations

N/A

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\(n35/27\) that is better than O\(n13/10\) of the best previously known algorithm by Magniez et al.

Why This Paper Matters

  • This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
  • It adds a 2011 reference point for readers tracking recent quantum research.
  • Besides the Hidden Subgroup Problem, the second large class of quantum speed-ups is for functions with constant-sized 1-certificates.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1105.4024 [2] arXiv https://arxiv.org/abs/1105.4024 [3] Publisher https://arxiv.org/abs/1105.4024

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