SIAM Journal on Computing
Introductory Combinatorics
Searching in Random Partially Ordered Sets
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
A Better Lower Bound for Quantum Algorithms Searching an Ordered List
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Bounds for Small-Error and Zero-Error Quantum Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Quantum versus Classical Learnability
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Graph entropy and quantum sorting problems
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Quantum Algorithms for Element Distinctness
SIAM Journal on Computing
Improved Bounds on Quantum Learning Algorithms
Quantum Information Processing
Generalization of Binary Search: Searching in Trees and Forest-Like Partial Orders
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Quantum search on bounded-error inputs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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We investigate the generalisation of quantum search of unstructured and totally orderedsets to search of partially ordered sets (posets). Two models for poset search are consid-ered. In both models, we show that quantum algorithms can achieve at most a quadraticimprovement in query complexity over classical algorithms, up to logarithmic factors; wealso give quantum algorithms that almost achieve this optimal reduction in complexity.In one model, we give an improved quantum algorithm for searching forest-like posets;in the other, we give an optimal O(√m)-query quantum algorithm for searching posetsderived from m×m arrays sorted by rows and columns. This leads to a quantum algo-rithm that finds the intersection of two sorted lists of n integers in O(√n) time, whichis optimal.