Physics – Quantum Physics
Scientific paper
2011-02-25
J. Phys. A: Math. Theor. 44, 255302 (2011)
Physics
Quantum Physics
27 pages, 1 figure
Scientific paper
10.1088/1751-8113/44/25/255302
An estimate is derived for the volume fraction of a subset $C_{\epsilon}^{P} = \{U : ||grad J(U)|\leq {\epsilon}\}\subset\mathrm{U}(N)$ in the neighborhood of the critical set $C^{P}\simeq\mathrm{U}(\mathbf{n})P\mathrm{U}(\mathbf{m})$ of the kinematic quantum ensemble control landscape J(U) = Tr(U\rho U' O), where $U$ represents the unitary time evolution operator, {\rho} is the initial density matrix of the ensemble, and O is an observable operator. This estimate is based on the Hilbert-Schmidt geometry for the unitary group and a first-order approximation of $||grad J(U)||^2$. An upper bound on these near-critical volumes is conjectured and supported by numerical simulation, leading to an asymptotic analysis as the dimension $N$ of the quantum system rises in which the volume fractions of these "near-critical" sets decrease to zero as $N$ increases. This result helps explain the apparent lack of influence exerted by the many saddles of $J$ over the gradient flow.
Dominy Jason
Rabitz Herschel
No associations
LandOfFree
Volume Fractions of the Kinematic "Near-Critical" Sets of the Quantum Ensemble Control Landscape does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Volume Fractions of the Kinematic "Near-Critical" Sets of the Quantum Ensemble Control Landscape, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Volume Fractions of the Kinematic "Near-Critical" Sets of the Quantum Ensemble Control Landscape will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-710145