Engineering coherent control of quantum information in spin systems

Quantum Information Processing (QIP) promises increased efficiency in computation. A key step in QIP is implementing quantum logic gates by engineering the dynamics of a quantum system. This thesis explores the requirements and methods of coherent control in the context of magnetic resonance for: (i) nuclear spins of small molecules in solution and (ii) nuclear and electron spins in single crystals. The power of QIP is compromised in the presence of decoherence. One method of protecting information from collective decoherence is to limit the quantum states to those respecting the symmetry of the noise. These decoherence-free subspaces (DFS) encode one logical quantum bit (qubit) within multiple physical qubits. In many cases, such as nuclear magnetic resonance (NMR), the control Hamiltonians required for gate engineering leak the information outside the DFS, whereby protection is lost: It is shown how one can still perform universal logic among encoded qubits in the presence of leakage. These ideas are demonstrated on four carbon-13 spins of a small molecule in solution. Liquid phase NMR has shortcomings for QIP, like the lack of strong measurement and low polarization. These two problems can be addressed by moving to solid-state spin systems and incorporating electron spins. If the hyperfine interaction has an anisotropic character, it is proven that the composite system of one electron and N nuclear spins (le-Nn) is completely controllable by addressing only to the electron spin. This 'electron spin actuator' allows for faster gates between the nuclear spins than would be achievable in its absence. In addition, a scheme using logical qubit encodings is proposed for removing the added decoherence due to the electron spin. Lastly, this thesis exemplifies arbitrary gate engineering in a le-ln ensemble solid-sate spin system using a home-built ESR spectrometer designed specifically for engineering high-fidelity quantum control.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Nuclear Science and Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Hodges, Jonathan Stuart

Advisor dc:contributor.advisor

• David G. Cory.

• Nuclear Science and 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/1721.1/44781

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/44781