| Summary: | 碩士 === 國立成功大學 === 航空太空工程學系 === 103 === Student: Chin-Wei Chaung
Advisor: Ciann-Dong Yang
Department of Aeronautics and Astronautics,National Cheng Kung University
ABSTRACT
This thesis intends to conquer the limitation of traditional qubit control that a single magnetic field can only control a single electron, by putting forward the idea of controlling multiple electrons (multiple quantum bits) via entanglement among them by a single magnetic field. No matter what number of electrons is involved, we show that the spin motion of multiple electrons can be described by a redefined Liouville equation and controlled by a Lyapunov-based control theory. With the introduction of the methods of path programming and Schmidt decomposition, the thesis successfully controls multiple electrons into an entangled state which allows quantum information between the electrons to be interchanged so that multiple electrons can be controlled as a whole by a single magnetic field. The entangled state is found to be vulnerable by a high-gain control. Once entanglement is lost, control of multiple electrons by a single magnetic field becomes impossible, no matter how large the control gain is. This thesis proposes several quantitative indices of entanglement to evaluate the ability of a control strategy to preserve quantum entanglement.
In addition, the thesis designs a series of optical experiments to prove the feasibility of the proposed idea of entangled control. As a final contribution, the thesis applies entangled control of multiple qubits to the field of quantum communication to realize mathematical quantum algorithms by practical engineering methods.
Keywords: Quantum Control, Entangled Control, Lyapunov Control, Liouville Equation, Relative Entropy, Entanglement Entropy.
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