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Modeling the evolution of open quantum systems
Pandey, Aditi
Pandey, Aditi
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2020-07
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The motivation for the research is to find a method to describe the evolution of an open single qubit system since the Schrödinger equation cannot be used. Therefore, to do this, the single qubit is first coupled to another qubit so that the joint system is closed. Next, a QMUX operation is applied on the joint system, after which the state of the first qubit is found (by tracing over the second qubit). The goal now is to find such a QMUX operation/s that can map the density matrix of the first qubit into any arbitrary density matrix by applying the QMUX and the partial trace operation. The aim is to cover the entire region of the Bloch sphere. However, it will be shown in this thesis, the entire region is not covered under one single QMUX operation, but an ellipsoid within the Bloch sphere. In this thesis, different QMUX operations and the regions covered within the Bloch sphere will be presented. As future work, combinations of QMUX operations will be studied such that the entire sphere can be covered. Here, there types of QMUX operations are considered: Type 1: QMUX with single rotation Type 2: QMUX with two rotation Type 3: QMUX with three rotation In this thesis, a detailed study is only performed on Type 1 QMUX operations. It is also shown how to calculate system parameters for a given Hamiltonian to implement these QMUX operations.
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Thesis (M.S.)-- Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science
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Wichita State University
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Copyright 2020 by Aditi Pandey
All Rights Reserved