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Optimized Quantum State Transitions

Scholtens, Robbert (2018) Optimized Quantum State Transitions. Bachelor's Thesis, Mathematics.


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The quantum brachistochrone problem -- to find the time-optimal transition between given initial and final quantum states -- is investigated in this bachelor's thesis. First the quantum equivalent of distance (the Fubini-Study metric) is formulated, using geometry of spheres. Together with constraints, it is used to create the quantum action. Functional derivatives are then taken of said action to find equations of motion (eoms). For the unconstrained case (excluding finite energy), these eoms are solved in closed form, whilst general to be solved formulae are obtained for the constrained case. The latter is used to explicitly solve an example quantum brachistochrone problem: a spin-1/2 particle in a controllable magnetic field constrained to an x-y plane. Finally, the link with quantum computing is illustrated through the time-optimization of unitary transformations that the quantum brachistochrone yields us.

Item Type: Thesis (Bachelor's Thesis)
Supervisor name: Waalkens, H. and Palasantzas, G.
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 20 Jul 2018
Last Modified: 23 Jul 2018 13:12

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