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Quantum Algorithms for the Triangle Problem
[article]

2005
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arXiv
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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

arXiv:quant-ph/0310134v3
fatcat:brszkmf4enfw7lrhn26zu3hpca