Quantum Algorithms for the Triangle Problem release_e6acwugt4zeebhhbq2uenxfur4

by Frederic Magniez, Miklos Santha, Mario Szegedy

Released as a article .

2003  

Abstract

We present two new quantum algorithms that either find a triangle (a copy of K_3) in an undirected graph G on n nodes, or reject if G is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes Õ(n^10/7) queries. The second algorithm uses Õ(n^13/10) queries, and it is based on a design concept of Ambainis amb04 that incorporates the benefits of quantum walks into Grover search gro96. The first algorithm uses only O( n) qubits in its quantum subroutines, whereas the second one uses O(n) qubits. The Triangle Problem was first treated in bdhhmsw01, where an algorithm with O(n+√(nm)) query complexity was presented, where m is the number of edges of G.
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Type  article
Stage   submitted
Date   2003-11-07
Version   v2
Language   en ?
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