Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 \frac{1}{\pi}(\ln(N)-1) accesses to the
list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary
comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary
comparisons for element distinctness. The previously best known lower bounds
are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}),
respectively. Our proofs are based on a weighted all-pairs inner product
argument.
  In addition to our lower bound results, we give a quantum algorithm for
ordered searching using roughly 0.631 \log_2(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 algorithm due
to Farhi, Goldstone, Gutmann, and Sipser.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc