Haase, Thorsten (2022)
On quantum state conversion in the constrained two-qubit system and its application to a reduced Rydberg-trimer model.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00022959
Dissertation, Erstveröffentlichung, Verlagsversion

Kurzbeschreibung (Abstract)

Preparing quantum states is essential for quantum information processing since any process must start at a well-defined initial state. State conversion describes techniques to transform a specific initial- into a predefined target state. This dissertation investigates quantum state conversion for two interacting qubits and its specialization to a constrained system where only adjacent levels are connected. Furthermore, it shows its applicability in a system of three qubits supposed to model interacting Rydberg atoms. A general Lie-algebraic approach is discussed, allowing a wide range of unitary transformations of the interacting two-qubit system to be described by two independent pseudospin degrees of freedom. Although restricting the representable transformations, the approach offers a simple description of many different conversion schemes and is well-suited to discuss the mentioned constrained situation. For this constrained Hamiltonian, a specific state conversion scheme is developed, which can be adopted in a reduced system of three qubits. These three qubits are supposed to model a Rydberg-atom trimer, and the developed conversion scheme maps onto the transformation between the three-atomic W state and the corresponding Greenberger-Horne-Zeilinger state. This mapping is achieved by reducing the eight-dimensional system to an effective four-level system. Two possible reduction schemes are presented. One depends on phase-matching conditions and the other on lifting degeneracies and employing multiple separated time scales in the eight-dimensional dynamics. The control over the atomic ensemble is established via the interaction with coherent states of the electromagnetic field. All topics are presented in the framework of quantum optics which is the theoretical foundation of much of the developing field of quantum technologies. The presented research shows how to design quantum state conversion protocols for two interacting qubits and apply such conversion protocols to more complex systems by employing reduction schemes. These reduction schemes allow for an effective description by lowering the dimension of the considered dynamics. The presented W to Greenberger-Horne-Zeilinger state conversion protocol in the Rydbergtrimer model outperforms previously proposed solutions for the same task.

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