Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discrete invitation to quantum filtering and feedback control   The engineering and control of devices at the quantum-mechanical level--such
as those consisting of small numbers of atoms and photons--is a delicate
business. The fundamental uncertainty that is inherently present at this scale
manifests itself in the unavoidable presence of noise, making this a novel
field of application for stochastic estimation and control theory. In this
expository paper we demonstrate estimation and feedback control of quantum
mechanical systems in what is essentially a noncommutative version of the
binomial model that is popular in mathematical finance. The model is extremely
rich and allows a full development of the theory, while remaining completely
within the setting of finite-dimensional Hilbert spaces (thus avoiding the
technical complications of the continuous theory). We introduce discretized
models of an atom in interaction with the electromagnetic field, obtain
filtering equations for photon counting and homodyne detection, and solve a
stochastic control problem using dynamic programming and Lyapunov function
methods.

30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph