The quantum Fourier transform and quantum chaos

In this thesis I study control of quantum systems while implementing complex quantum operations. Through experimental implementations of such operations, I test the accuracy of control and provide methods for identifying the type and strength of experimental errors. The centerpiece of this work is the quantum Fourier transform (QFT), an essential gate for quantum algorithms and quantum simulations. Experiments are performed on a three qubit liquid-state nuclear magnetic resonance quantum information processor, and demonstrate salient features of the QFT in both of these venues. The first experiment exhibits the ability of the QFT to extract periodicity, a necessary process for many quantum algorithms. As an example of a quantum simulation, I implement a three qubit quantum baker's map, which is composed of QFTs, and discuss how various conjectures of quantum chaos could be experimentally realized on a quantum computer. Another example of complex quantum operations are 'pseudo-random' maps. These are operators which pass statistical tests of randomness but can be efficiently implemented on a quantum computer. I explore the importance of pseudo-random maps for the study of quantum chaos and a host of quantum information processing protocols. I also implement a set of such maps experimentally. In order to determine the type and strength of the errors effecting our implemetations, quantum process tomography is done on the QFT.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Nuclear Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Weinstein, Yaakov Shmuel, 1974-

Advisor dc:contributor.advisor

• David G. Corey.

• Nuclear Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/17023

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/17023