Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Quantum Search by Parallel Unitary Discrimination Schemes   We study the unsorted database search problem with items $N$ from the
viewpoint of unitary discrimination. Instead of considering the famous
$O(\sqrt{N})$ Grover's the bounded-error algorithm for the original problem, we
seek for the results about the exact algorithms, i.e. the ones succeed with
certainty. Under the standard oracle model $\sum_j (-1)^{\delta_{\tau j}}|j><
j|$, we demonstrate a tight lower bound ${2/3}N+o(N)$ of the number of queries
for any parallel scheme with unentangled input states. With the assistance of
entanglement, we obtain a general lower bound ${1/2}(N-\sqrt{N})$. We provide
concrete examples to illustrate our results. In particular, we show that the
case of N=6 can be solved exactly with only two queries by using a bipartite
entangled input state. Our results indicate that in the standard oracle model
the complexity of exact quantum search with one unique solution can be strictly
less than that of the calculation of OR function.

14
The categories of this paper are: math-ph
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The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics