Quantum Algorithms for the Triangle Problem [article]

Frederic Magniez, Miklos Santha, Mario Szegedy
2005 arXiv   pre-print
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
more » ... e 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.
arXiv:quant-ph/0310134v3 fatcat:brszkmf4enfw7lrhn26zu3hpca