On the hitting times of quantum versus random walks
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Claw finding algorithms using quantum walk
Theoretical Computer Science
Quantum random walks - new method for designing quantum algorithms
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Quantum walks with multiple or moving marked locations
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Quantum property testing for bounded-degree graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
SIAM Journal on Computing
Improved output-sensitive quantum algorithms for Boolean matrix multiplication
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Span programs for functions with constant-sized 1-certificates: extended abstract
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Improving quantum query complexity of boolean matrix multiplication using graph collision
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Quantum counterfeit coin problems
Theoretical Computer Science
Quantum walks: a comprehensive review
Quantum Information Processing
The quantum query complexity of read-many formulas
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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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 $\tilde{O}(n^{10/7})$ queries. The second algorithm uses $\tilde{O}(n^{13/10})$ queries and is based on a design concept of Ambainis [in Proceedings of the $45$th IEEE Symposium on Foundations of Computer Science, 2004, pp. 22-31] that incorporates the benefits of quantum walks into Grover Search [L. Grover, in Proceedings of the Twenty-Eighth ACM Symposium on Theory of Computing, 1996, pp. 212-219]. The first algorithm uses only $O(\log n)$ qubits in its quantum subroutines, whereas the second one uses $O(n)$ qubits. The Triangle Problem was first treated in [H. Buhrman et al., SIAM J. Comput., 34 (2005), pp. 1324-1330], where an algorithm with $O(n+\sqrt{nm})$ query complexity was presented, where $m$ is the number of edges of $G$.