Abstract
This chapter is devoted to describe Hamilton formalism for studying superconducting quantum bits (qubits). The first section is devoted to discuss phase, charge and flux qubits separately. For the realization of qubit operations based on JJ and their application requires the mK temperature regions. As followed from Chap. 1, anharmonic character of CPR becomes important at this temperatures and as result anharmonicity must be taken into account in consideration of JJ qubits. For this reason the influence of anharmonic CPR on qubit characteristics presented in Sect. 4.2. Description of silent qubit using anharmonic CPR given in Sect. 4.3. Flux qubit based on three JJ analyzed in Sect. 4.4. Section 4.5 is devoted to adiabatic measurements and Rabi oscillations in superconducting qubits is in Sect. 4.6.
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