Advanced dynamical decoupling strategies for simulating Hamiltonian interactions
In the field of quantum information, a major challenge is to protect and shield quantum systems from environmental influences, which cause dissipation and decoherence. One approach to address this problem is called dynamical decoupling, where we act on a quantum system with a series of fast and stro...
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| Format: | Others |
| Language: | German en |
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2016
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| Online Access: | https://tuprints.ulb.tu-darmstadt.de/5233/1/dissertation_frydrych_2016.pdf Frydrych, Holger <http://tuprints.ulb.tu-darmstadt.de/view/person/Frydrych=3AHolger=3A=3A.html> (2016): Advanced dynamical decoupling strategies for simulating Hamiltonian interactions.Darmstadt, Technische Universität Darmstadt, [Ph.D. Thesis] |
| Summary: | In the field of quantum information, a major challenge is to protect and shield quantum systems from environmental influences, which cause dissipation and decoherence. One approach to address this problem is called dynamical decoupling, where we act on a quantum system with a series of fast and strong local control operations. If done correctly, the system's state gets rotated in discrete steps in its state space in such a way that the effects of the environment cancel up to a certain order. In the first part of this thesis, we will introduce the basics of dynamical decoupling and present a new approach for constructing dynamical decoupling schemes based on sequences of Weyl operators on networks of qudits. This approach goes beyond merely protecting a quantum system, as it is also capable of altering existing Hamiltonian interactions in ways suitable for quantum simulation purposes. We will also investigate how imperfect controls influence the effectiveness of dynamical decoupling and focus particularly on stochastic noise.
In the second part of the thesis, we study concrete scenarios for the application of dynamical decoupling. First, we consider the task of quantum state transfer on a linear chain of qubits and use decoupling to protect the transfer from detrimental influences caused by a bend in the chain. We also look at how to design the specific interaction strengths required on the chain to make the state transfer work and extend this result to chains of qudits. Another chapter deals with decoupling the atomic centre-of-mass motion of a trapped atom or ion in a cavity interacting with a radiation field. Finally, we use decoupling to execute sequences of one- and two-qubit quantum gates on a chain of coupled qubits. Particular care is taken to ensure high fidelity operations in the presence of imperfect decoupling pulses. |
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