Quantum decoherence by chaotic environments: theory and applications

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(Thesis) Ph.D.
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Condensed and solid phase environments offer a wide range of controllable interactions for new quantum technologies. Understanding the dynamics of open quantum systems interacting with such complex environments is important for correct modeling of many chemical and physical phenomena and for development of new quantum technologies. The central theme of this thesis is the open system dynamics of a small quantum system coupled to self-interacting chaotic environments. This thesis consists of three related parts. In the first part, a theory predicting open dynamics of a quantum system interacting with chaotic environments is reported. The theory is of a Kraus decomposition form, which is exact for chaotic environments of thermodynamic dimension. Extension of the theory to time-dependent system Hamiltonians is also presented so that it may have practical applications for studies of new quantum technologies. In the second part, extensive numerical calculations are performed to obtain the exact quantum dynamics for two realistic models of self-interacting environments. Both models represent a statistically flawed isolated quantum computer (QC) core. In the first model, the open dynamics of a quantum-control NOT (CNOT) gate in the presence of static internal imperfections are investigated and internal error sources are identified for a large number of QC configurations. The results indicate that the strong two-body imperfections suppress the internal decoherence and enhance the performance of the CNOT gate. Moreover, the largest source of error is found to be unitary due to coherent shifting rather than decoherence. The second model represents a single-qubit detector set-up designed to probe the internal bath dynamics. Small low temperature isolated QCs with static internal flaws can be considered as prototypical examples of self-interacting - and possibly chaotic - environments of two level systems for which the exact quantum dynamics can be numerically tractable on a classical computer. In the third part, the theory of chaotic environments is tested against the exact numerical results of the above models and very good agreements are obtained.
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