Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Claw finding algorithms using quantum walk
Theoretical Computer Science
Element distinctness and sorting on one-tape off-line turing machines
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Quantum search of partially ordered sets
Quantum Information & Computation
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
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
An improved claw finding algorithm using quantum walk
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Optimal randomized comparison based algorithms for collision
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
| Hi-index | 0.00 |
We present several applications of quantum amplitude amplification for deciding whether all elements in the image of a given function are distinct, for finding an intersection of two sorted tables, and for finding a triangle in a graph. Our techniques generalize and improve those of Brassard, Hoyer, and Tapp [ACM SIGACT News, 28 (1997), pp. 14--19]. This shows that in the quantum world element distinctness is significantly easier than sorting, in contrast to the classical world.