A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On the Power of Quantum Computation
SIAM Journal on Computing
Quantum simulations of classical random walks and undirected graph connectivity
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum lower bound for the collision problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Lower Bounds for the Collision and the Element Distinctness Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Bounds for Small-Error and Zero-Error Quantum Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Classical and Quantum Computation
Classical and Quantum Computation
Quantum Algorithms for Element Distinctness
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Polynomial Degree vs. Quantum Query Complexity
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Quantum Walk Algorithm for Element Distinctness
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
ACM SIGACT News
Coins make quantum walks faster
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum verification of matrix products
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Polynomial degree vs. quantum query complexity
Journal of Computer and System Sciences - Special issue on FOCS 2003
Improved algorithms for quantum identification of Boolean oracles
Theoretical Computer Science
Negative weights make adversaries stronger
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
The quantum query complexity of the determinant
Information Processing Letters
Recent progress in quantum algorithms
Communications of the ACM
The quantum complexity of group testing
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
A note on the search for k elements via quantum walk
Information Processing Letters
Finding is as easy as detecting for quantum walks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Efficient circuits for quantum walks
Quantum Information & Computation
Quantum walks on directed graphs
Quantum Information & Computation
All quantum adversary methods are equivalent
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Promised and distributed quantum search
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
The quantum query complexity of algebraic properties
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
An improved claw finding algorithm using quantum walk
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Span programs and quantum algorithms for st-connectivity and claw detection
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Discrete-time interacting quantum walks and quantum Hash schemes
Quantum Information Processing
Quipper: a scalable quantum programming language
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Line ordering of reversible circuits for linear nearest neighbor realization
Quantum Information Processing
| Hi-index | 0.02 |
We present two new quantum algorithms that either find a triangle (a copy of K3) 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(n10/7) queries. The second algorithm uses Õ(n13/10) queries, and it is based on a new design concept of Ambainis [6] that incorporates the benefits of quantum walks into Grover search [18]. 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 [12], where an algorithm with O(n + √n|E|) query complexity was presented (here |E| is the number of edges of G).