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Study of synchronization of Qubits: manifestation of quantum effects

Polidis Petros

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Year 2020
Type of Item Diploma Work
Bibliographic Citation Petros Polidis, "Study of synchronization of Qubits: manifestation of quantum effects", Diploma Work, School of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece, 2020
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This work deals with the phenomenon of synchronization, (a well-known effect in the field of nonlinearly interacting multiparticle classical systems formulated by the so called Kuramodo model) , and the question of its possible interrelation with quantum effects, addressed in the minimal context of two interacting qubits. The aim of the work is to review available recent research results both in the fields of classical synchronization and multi-qubit systems. This shapes the form of the thesis as a comprehensive review of some of the available analytic-numerical results, methods and concepts, regarding the question of the synchronization effect in the presence of pair of qubits. In outline the content of the thesis is as follows: a pair of special qubits each described by a 2D complex vector with a simple azimuthal angle freedom (the equatorial qubit), are employed. A sequence of quantum gate operators, codified in the form of a quantum circuit, is utilized to show that the temporal dynamics of the qubit state vectors is governed by the Kuramoto models via their azimuthal angles. A matrix observable, the “quantum synchronization” operator, and the “quantum dispersion” observable are introduced. These observables combined with solutions of the Kuramoto driven state vectors for the pair of interacting equatorial qubits, are able to quantify the quantum effects of the classical synchronization measures. The resulting ‘quantum mean value’ and the quantum dispersion value of the qubit-qubit synchronization is studied by numerically plotting their variation for four important special cases: the temporally varying, or temporally constant (stationary), qubit states vectors, as well as the un-correlated pair of equatorial qubits described by pure states, and the uncorrelated pair of thermal equatorial qubits described by mixed states; as well as possible combinations of these special cases. In accordance to the available results of qubit-synchronization it is confirmed that the two-body synchronization survives in the qubit context. This is manifested by the non-zero value of the “quantum synchronization” operator, and its non-zero but bounded and asymptotically constant dispersion (quantum uncertainty).

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