Superconducting Qubit Software, Design Tools & Theory
Bottom-up Modeling of Superconducting Qubits
11:42 am – 11:54 amWe provide a framework for modelling of noise in superconducting qubits based on the microscopic theory of superconductivity, as opposed to the conventional approach based on cQED.
The starting point for the modelling are the BCS Hamiltonian and the Bogoliubov-de Gennes formalism, which allows for the modelling of Josephson junctions as SNS or SIS junctions.
We use analytical solutions to the Bogoliubov equations in combination with a numerical approach to obtain self-consistent solutions for the quasiparticle spectrum.
These solutions allow for a direct analysis of Andreev states and tunnelling properties of the junction, which in turn allows the calculation of the nonlinear inductance.
The nonlinear inductance also appears in the cQED formulation, as the potential for the qubit state in the phase basis -- it is precisely this nonlinearity that allows the qubit levels to be isolated.
Thus, we connect the microscopic and macroscopic pictures of superconducting qubits, and provide a framework for the analysis of effects of noise and geometry on qubit properties.