Claw finding algorithms using quantum walk

The claw finding problem has been studied in terms of query complexity as one of the problems closely connected to cryptography. Given two functions, f and g , with domain sizes N and M ( N ≤ M ) , respectively, and the same range, the goal of the problem is to find x and y such that f ( x ) = g ( y...

Full description

Saved in:
Bibliographic Details
Published inTheoretical computer science Vol. 410; no. 50; pp. 5285 - 5297
Main Author Tani, Seiichiro
Format Journal Article
LanguageEnglish
Published Elsevier B.V 17.11.2009
Subjects
Oracle computation
Quantum computing
Quantum walk
Query complexity
Quantum computing
Query complexity
Quantum walk
Oracle computation
Online AccessGet full text

Cover

More Information
Summary:The claw finding problem has been studied in terms of query complexity as one of the problems closely connected to cryptography. Given two functions, f and g , with domain sizes N and M ( N ≤ M ) , respectively, and the same range, the goal of the problem is to find x and y such that f ( x ) = g ( y ) . This problem has been considered in both quantum and classical settings in terms of query complexity. This paper describes an optimal algorithm that uses quantum walk to solve this problem. Our algorithm can be slightly modified to solve the more general problem of finding a tuple consisting of elements in the two function domains that has a prespecified property. It can also be generalized to find a claw of k functions for any constant integer k > 1 , where the domain sizes of the functions may be different.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2009.08.030