In this thesis, two aspects of control theory, namely
controllability and optimal control, are applied to quantum
systems. The presented results are based on group theoretical
techniques and numerical studies. By Lie-algebraic analysis, the
controllability properties of systems with an arbitrary topology
are described and related to the symmetries existing in these
systems. We find that symmetry precludes full controllability. Our
work investigates well-known control systems and gives rules for
the design of new systems. Furthermore, theoretical and numerical
concepts are instrumental to studying quantum channels: Their
capacities are optimised using gradient flows on the unitary group
in order to find counterexamples to a long-established additivity
conjecture. The last part of this thesis presents and benchmarks a
modular optimal control algorithm known as GRAPE. Numerical tests
show how the interplay of its modules can be optimised for higher
performance, and how the algorithm performs in comparison to a
Krotov-type optimal control algorithm. It is found that GRAPE
performs particularly well when aiming for high qualities.
General
Imprint: |
Sudwestdeutscher Verlag Fur Hochschulschriften AG
|
Country of origin: |
United States |
Release date: |
March 2011 |
First published: |
March 2011 |
Authors: |
Uwe Sander
|
Dimensions: |
229 x 152 x 9mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
148 |
ISBN-13: |
978-3-8381-2484-1 |
Categories: |
Books >
Science & Mathematics >
Physics >
General
|
LSN: |
3-8381-2484-7 |
Barcode: |
9783838124841 |
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