One-Dimensional Continuous-Time Quantum Walks
Quantum Information Processing
The Quantum Complexity of Markov Chain Monte Carlo
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Efficient discrete-time simulations of continuous-time quantum query algorithms
Proceedings of the forty-first annual ACM symposium on Theory of computing
Claw finding algorithms using quantum walk
Theoretical Computer Science
Recent progress in quantum algorithms
Communications of the ACM
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
Tree search and quantum computation
Quantum Information Processing
Eigenpath traversal by phase randomization
Quantum Information & Computation
Quantum Information & Computation
Merkle puzzles in a quantum world
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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
Improved output-sensitive quantum algorithms for Boolean matrix multiplication
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Exact Quantum Algorithms for the Leader Election Problem
ACM Transactions on Computation Theory (TOCT)
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
The quantum query complexity of AC0
Quantum Information & Computation
Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
Quantum Information Processing
Span programs and quantum algorithms for st-connectivity and claw detection
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Adversary lower bound for the k-sum problem
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Discrete-time interacting quantum walks and quantum Hash schemes
Quantum Information Processing
Superlinear advantage for exact quantum algorithms
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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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 $O(N^{2/3})$ query quantum algorithm. This improves the previous $O(N^{3/4})$ quantum algorithm of Buhrman et al. [SIAM J. Comput., 34 (2005), pp. 1324-1330] and matches the lower bound of Aaronson and Shi [J. ACM, 51 (2004), pp. 595-605]. We also give an $O(N^{k/(k+1)})$ query quantum algorithm for the generalization of element distinctness in which we have to find $k$ equal items among $N$ items.