Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Control Landscapes: A Closer Look   The control landscape for various canonical quantum control problems is
considered. For the class of pure-state transfer problems, analysis of the
fidelity as a functional over the unitary group reveals no suboptimal
attractive critical points (traps). For the actual optimization problem over
controls in $L^2(0,T)$, however, there are critical points for which the
fidelity can assume any value in (0,1), critical points for which the second
order analysis is inconclusive, and traps. For the class of unitary operator
optimization problems analysis of the fidelity over the unitary group shows
that while there are no traps over U(N), traps already emerge when the domain
is restricted to the special unitary group. The traps on the group can be
eliminated by modifying the performance index, corresponding to optimization
over the projective unitary group. However, again, the set of critical points
for the actual optimization problem for controls in $L^2(0,T)$ is larger and
includes traps, some of which remain traps even when the target time is allowed
to vary.

15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an