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Discrete quantum control.

University of California, San Diego., Mathematics.

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Discrete quantum control.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Discrete quantum control./
Author:	Grice, Jon R.
Description:	107 p.
Notes:	Adviser: David A. Meyer.
Contained By:	Dissertation Abstracts International70-01B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3341872
ISBN:	9780549981466

Discrete quantum control.
Grice, Jon R.

Discrete quantum control. - 107 p.

Adviser: David A. Meyer.

Thesis (Ph.D.)--University of California, San Diego, 2009.

This dissertation is a study of several aspects of discrete time quantum control. After reviewing the necessary background from quantum mechanics and control theory we construct a simple model and solve a control problem on it as a proof of concept for the discrete control formulation developed herein. We apply optimal control to solve a state preparation problem on a physically motivated time discretized single qubit system with simplified dynamics to enable the Bellman equation to be solved both numerically and approximately analytically. However for more than one qubit classical theories of control become problematic, a notable difficulty being the exponential increase in the size of the state space with the number of particles. To study workarounds for this problem we quantify how much information a quantum measurement can extract from the system and then use the results to show that a naive classical technique for controlling a multiparticle system performs poorly when the system has "quantum" properties. We then consider the problem of protecting the entanglement of a bipartite quantum system using discrete open loop control with a technique that seems to have no classical analog. The states of the bipartite system, called X-states, have a special structure which is generalized to states of systems with more than two qubits. We develop the properties of these generalized X-states which are a class of mixed states with interesting multipartite entanglement properties.

ISBN: 9780549981466Subjects--Topical Terms:

515831
Mathematics.

Discrete quantum control.
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020 $a 9780549981466
035 $a (UMI)AAI3341872
035 $a AAI3341872
040 $a UMI $c UMI
100 1 $a Grice, Jon R. $3 1022365
245 1 0 $a Discrete quantum control.
300 $a 107 p.
500 $a Adviser: David A. Meyer.
500 $a Source: Dissertation Abstracts International, Volume: 70-01, Section: B, page: 0329.
502 $a Thesis (Ph.D.)--University of California, San Diego, 2009.
520 $a This dissertation is a study of several aspects of discrete time quantum control. After reviewing the necessary background from quantum mechanics and control theory we construct a simple model and solve a control problem on it as a proof of concept for the discrete control formulation developed herein. We apply optimal control to solve a state preparation problem on a physically motivated time discretized single qubit system with simplified dynamics to enable the Bellman equation to be solved both numerically and approximately analytically. However for more than one qubit classical theories of control become problematic, a notable difficulty being the exponential increase in the size of the state space with the number of particles. To study workarounds for this problem we quantify how much information a quantum measurement can extract from the system and then use the results to show that a naive classical technique for controlling a multiparticle system performs poorly when the system has "quantum" properties. We then consider the problem of protecting the entanglement of a bipartite quantum system using discrete open loop control with a technique that seems to have no classical analog. The states of the bipartite system, called X-states, have a special structure which is generalized to states of systems with more than two qubits. We develop the properties of these generalized X-states which are a class of mixed states with interesting multipartite entanglement properties.
590 $a School code: 0033.
650 4 $a Mathematics. $3 515831
650 4 $a Physics, Theory. $3 1019422
690 $a 0405
690 $a 0753
710 2 $a University of California, San Diego. $b Mathematics. $3 1022364
773 0 $t Dissertation Abstracts International $g 70-01B.
790 $a 0033
790 1 0 $a Fogler, Michael $e committee member
790 1 0 $a Helton, William $e committee member
790 1 0 $a Meyer, David A., $e advisor
790 1 0 $a Sham, Lu J. $e committee member
790 1 0 $a Wallach, Nolan $e committee member
791 $a Ph.D.
792 $a 2009
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3341872