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DYNAMICAL ERROR SUPPRESSION FOR QUANTUM INFORMATION
PROCESSING
by
Kaveh Khodjasteh Lakelayeh
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PHYSICS)
August 2007
Copyright 2007 Kaveh Khodjasteh Lakelayeh
Object Description
| Title | Dynamical error suppression for quantum information |
| Author | Khodjasteh Lakelayeh, Kaveh |
| Author email | khodjast@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Thesis |
| Degree program | Physics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2007-06-12 |
| Date submitted | 2007 |
| Restricted until | Unrestricted |
| Date published | 2007-07-27 |
| Advisor (committee chair) | Lidar, Daniel A. |
| Advisor (committee member) |
Brun, Todd A. Haas, Stephan Däppen, Werner Lu, Grace Jia |
| Abstract | Quantum information theory is based on the premise of manipulating quantum systems. Decoherence and noisy control directly limit this manipulation. Quantum error correction theory aims to understand the sources of errors in manipulation of quantum systems and to remedy the problems caused by the errors in an efficient manner. In this thesis I focus on error correction mechanisms that are based on a realistic and physical picture of the interactions of the quantum system with the environment. In chapters 1, 2, and 3, I provide a brief introduction to quantum information processing, quantum error correction, and dynamical decoupling. In chapters 4 and 5, I consider error correction of a set of qubits in the presence of spontaneous emission as the main source of errors. These results have been published in [KL:02] and [KL:03]. The quantum trajectories picture is used for describing the error processes. Two error correction schemes are provided in this scenario and are both built on simple quantum error detecting codes for detecting quantum jump errors. The qubit number overhead in this encoding is reduced in the first method [KL:02] by exploiting the symmetry of the conditional dynamics that can be used to create a decoherence free subspace. In the second method [KL:03], the conditional dynamics is canceled by applying parallel population swapping operations on the qubits. For both methods, I describe means of integrating the proposed error correction schemes with various proposals to achieve fault tolerant quantum computation. Chapters 6 and 7 are based on dynamical decoupling: a method for removal of undesired interaction terms from a Hamiltonian evolution by application of fixed unitary quantum operators. These results have been published in [KL:05] and [KL:06]. I describe general concatenated pulse sequences that are constructed recursively from simple dynamical decoupling pulse sequences.; I show that using the concatenated dynamical decoupling sequences is (i) significantly more efficient than repeating traditional sequences and (ii) these sequences are more robust with respect to natural control errors [KL05a]. A comprehensive leading order analysis of dynamical decoupling efficiency is provided in the process [KL06]. In chapter 8 (not yet published), I describe the construction of selfcorrecting pulse sequences for a single qubit. |
| Keyword | quantum; quantum open systems; quantum information; quantum error corrrection; dynamical decoupling; quantum control; quantum error correcting coes |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m706 |
| Rights | Khodjasteh Lakelayeh, Kaveh |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-KhodjastehLakelayeh-20070727 |
| Archival file | uscthesesreloadpub_Volume62/etd-KhodjastehLakelayeh-20070727.pdf |
Description
| Title | Page 1 |
| Full text | DYNAMICAL ERROR SUPPRESSION FOR QUANTUM INFORMATION PROCESSING by Kaveh Khodjasteh Lakelayeh A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHYSICS) August 2007 Copyright 2007 Kaveh Khodjasteh Lakelayeh |
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