Browsing by Author "Heidebrecht, Andreas"

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Quantum-state-engineering for spin-quantum-computing
(2006) Heidebrecht, Andreas; Mehring, Michael (Prof. Dr.)
The subject of this thesis are experimental procedures for preparation, manipulation, and detection of specific quantum states of spin systems in the context of quantum computing. Nuclear magnetic resonance (NMR) and electron spin resonance (ESR) methods were used. The systems studied were small molecules in liquid state, small molecules embedded in a liquid crystal matrix, and paramagnetic centers in single crystals. The nuclear 19F spins of 2,3,4-Trifluoroaniline were used as qubits to implement the three-qubit Deutsch-Josza algorithm using high-resolution NMR. A classification of the Deutsch-Josza functions according to the operator representation of the corresponding oracle transformations was given. Different classes of functions may produce full, partial or no entanglement in the output states of the algorithm. This entanglement content is not immediately evident from the output states themselves. A procedure was given for mapping of the output states onto Bell- or GHZ-states by means of local transformations which preserve the entanglement content. A method for the visualization of single-spin unitary transformations was also presented. This visual representation can facilitate analysis and design of shaped rf pulses. For the purpose of quantum computing, it can be useful to suppress couplings between qubits during the application of finite-length single-qubit gates. The feasibility of this idea was demonstrated using small molecules in a liquid crystal matrix. In a series of proof-of-principle experiments, it was shown that the magic-echo sequence can be used to suppress the dipole-dipole coupling between spins and simultaneously selectively address a single spin by a soft rf pulse. The S-bus concept for spin-quantum computing holds some scalability promise and provides a testbed for studies of large, strongly coupled quantum registers. Single-crystal CaF2 weakly doped with Ce was used to implement the concept. The nine 19F nuclear spins adjacent to the paramagnetic Ce-ion serve as qubits while the electron spin plays the role of a quantum bus. The S-bus theory was tested experimentally. Procedures were given for the measurement of parameters characterizing the quantum state of the nuclear spins. An exact numeric treatment of this ten-spin system was done to aid in understanding the experimental findings. For a pair of nuclear spins with negligible direct dipolar coupling, the CNOT operation was implemented. The spin-spin coupling mediated by the bus spin was utilized for that purpose. The four Bell-states of these two distant spins were created. An experiment was performed who's signature allows those four entangled states to be distinguished. The paramagnetic cluster in CaF2:Ce is embedded in an extended network of 19F nuclear spins. This network is a powerful source of decoherence. A number of existing and a newly designed pulse sequence were tested with respect to their ability to suppress decoherence and their aptitude for use in quantum computing.