Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of Grover's quantum search algorithm as a dynamical system   Grover's quantum search algorithm is analyzed for the case in which the
initial state is an arbitrary pure quantum state $|\phi>$ of $n$ qubits. It is
shown that the optimal time to perform the measurement is independent of $|
\phi>$, namely, it is identical to the optimal time in the original algorithm
in which $| \phi > = | 0>$, with the same number of marked states, $r$. The
probability of success $P_{\rm s}$ is obtained, in terms of the amplitudes of
the state $| \phi>$, and is shown to be independent of $r$. A class of states,
which includes fixed points and cycles of the Grover iteration operator is
identified. The relevance of these results in the context of using the success
probability as an entanglement measure is discussed. In particular, the
Groverian entanglement measure, previously limited to a single marked state, is
generalized to the case of several marked states.

14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int