Dokument

Summary:
Quantum computing using the control techniques of nuclear magnetic resonance (NMR) has been one of the first experimental implementations of quantum informa- tion processing. By rotating nuclear spins inside molecules with magnetic fields, it is possible to implement any unitary operation on a set of spin-1/2-qubits. Since published work has so far been limited to the Ising spin interaction, this thesis extends the framework of NMR quantum computing to the Heisenberg interaction. In order to find NMR pulse sequences that represent quantum gates in the machine language of NMR quantum computing, magnetic and radio-frequency fields, an algorithm was implemented to examine billions of possible sequences for a universal set of quantum gates. The Python program was optimized to avoid the numerically most expensive calculations so that sequences up to nine pulses could be investigated. The search yielded an NMR pulse sequence for the anisotropic Heisenberg interaction that im- plements the CNOT quantum gate on an arbitrary input state. However, no such sequence was found for the isotropic Heisenberg interaction for a sequence of up to nine pulses in length and while restricting the single-qubit rotations to a finite set of rotation angles. The framework of NMR quantum computing can thus be extended to the Heisenberg interaction although it is not clear if universal quantum computing is possible using only the isotropic Heisenberg interaction to entangle two qubits.

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