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We show that the quantum query complexity of detecting if an $n$-vertex graph contains a triangle is $O(n^{9/7})$.
A fast quantum mechanical algorithm for database search
Lov K. Grover · 1996
Earlier work this paper cites.
Algorithms for quantum computation: Discrete logarithm and factoring
P. Shor · 1997
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Lower bounds on quantum query complexity
P. Høyer and R. Špalek · 2005
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Negative weights make adversaries stronger
Peter Høyer, Troy Lee, and Robert Špalek · 2007
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Quantum algorithms for the triangle problem
F. Magniez, M. Santha, and M. Szegedy · 2007
Earlier work this paper cites.
The quantum complexity of group testing
S. Dörn and T. Thierauf · 2008
Cited alongside, same era.
Quantum algorithm for k-distinctness with prior knowledge on the input
A. Belovs and T. Lee · 2011
Cited alongside, same era.
Personal Communication, 2011
R. Kothari · 2011
Cited alongside, same era.
A learning graph based quantum query algorithm for finding constant-size subgraphs
T. Lee, F. Magniez, and M. Santha · 2011
Cited alongside, same era.
Reflections for quantum query algorithms
Ben W. Reichardt · 2011
Later among the works it cites.
Quantum query complexity of subgraph containment with constant-sized certificates
Y. Zhu · 2011
Later among the works it cites.
Learning-graph-based quantum algorithm for k-distinctness
A. Belovs · 2012
Closest in time.
Span programs for functions with constant-sized 1-certificates
A. Belovs · 2012
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