Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight bounds on quantum searching   We provide a tight analysis of Grover's recent algorithm for quantum database
searching. We give a simple closed-form formula for the probability of success
after any given number of iterations of the algorithm. This allows us to
determine the number of iterations necessary to achieve almost certainty of
finding the answer. Furthermore, we analyse the behaviour of the algorithm when
the element to be found appears more than once in the table and we provide a
new algorithm to find such an element even when the number of solutions is not
known ahead of time. Using techniques from Shor's quantum factoring algorithm
in addition to Grover's approach, we introduce a new technique for approximate
quantum counting, which allows to estimate the number of solutions. Finally we
provide a lower bound on the efficiency of any possible quantum database
searching algorithm and we show that Grover's algorithm nearly comes within a
factor 2 of being optimal in terms of the number of probes required in the
table.

3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess