Coins make quantum walks faster
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum algorithms for the triangle problem
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
On the power of Ambainis lower bounds
Theoretical Computer Science
Improved algorithms for quantum identification of Boolean oracles
Theoretical Computer Science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Optimal computation with non-unitary quantum walks
Theoretical Computer Science
On the hitting times of quantum versus random walks
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The quantum query complexity of the determinant
Information Processing Letters
Coined quantum walks lift the cospectrality of graphs and trees
Pattern Recognition
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
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
Spatial search on a honeycomb network
Mathematical Structures in Computer Science
Efficient circuits for quantum walks
Quantum Information & Computation
Quantum algorithms for subset finding
Quantum Information & Computation
Quantum walks on directed graphs
Quantum Information & Computation
Exploring scalar quantum walks on Cayley graphs
Quantum Information & Computation
SIAM Journal on Computing
All quantum adversary methods are equivalent
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Quantum complexity of testing group commutativity
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
Towards unitary representations for graph matching
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
Coined quantum walks lift the cospectrality of graphs and trees
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Entanglement for discrete-time quantum walks on the line
Quantum Information & Computation
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
Time averaged distribution of a discrete-time quantum walk on the path
Quantum Information Processing
Quantum walks: a comprehensive review
Quantum Information Processing
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
Time-Efficient quantum walks for 3-distinctness
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Decoherence in quantum Markov chains
Quantum Information Processing
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We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an 0(n^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}}) query quantum algorithm. This improves the previous 0(n^{{3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-\nulldelimiterspace} 4}} ) quantum algorithm of Buhrman et al. [10] and matches the lower bound by Shi [28]. We also give an 0(N^{{k \mathord{\left/ {\vphantom {k {(k + 1)}}} \right. \kern-\nulldelimiterspace} {(k + 1)}}} ) query quantum algorithm for the generalization of element distinctness in which we have to find k equal items among N items.