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ICALP
2001
Springer

Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness

8 years 10 months ago
Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list, we prove a lower bound of 1 π (ln(N) − 1) accesses to the list elements for ordered searching, a lower bound of Ω(N log N) binary comparisons for sorting, and a lower bound of Ω( √ N log N) binary comparisons for element distinctness. The previously best known lower bounds are 1 12 log2(N) − O(1) due to Ambainis, Ω(N), and Ω( √ N), respectively. Our proofs are based on a weighted all-pairs inner product argument. In addition to our lower bound results, we give an exact quantum algorithm for ordered searching using roughly 0.631 log2(N) oracle accesses. Our algorithm uses a quantum routine for traversing through a binary search tree faster than classically, and it is of a nature very different from a faster exact algorithm due to F...
Peter Høyer, Jan Neerbek, Yaoyun Shi
Added 29 Jul 2010
Updated 29 Jul 2010
Type Conference
Year 2001
Where ICALP
Authors Peter Høyer, Jan Neerbek, Yaoyun Shi
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