Modeling and Harmonic Balance Analysis of Parametric Amplifiers for Qubit Read-out

Predicting the performance of traveling-wave parametric amplifiers (TWPAs) based on nonlinear elements like superconducting Josephson junctions (JJs) is vital for qubit read-out in quantum computers. The purpose of this article is twofold: (a) to demonstrate how nonlinear inductors based on combinations of JJs can be modeled in commercial circuit simulators, and (b) to show how the harmonic balance (HB) is used in the reliable prediction of the amplifier performance e.g., gain and pump harmonic power conversion. Experimental characterization of two types of TWPA architectures is compared with simulations to showcase the reliability of the HB method. We disseminate the modeling know-how and techniques to new designers of parametric amplifiers.

Extracting the Dispersion of Periodic Lossless LC Circuits Using the White Noise

The spectral energy density (SED) method is used to obtain the phonon dispersion of solids in molecular dynamics tools, e.g., LAMMPS. We show how the electric analog of the SED method is used to find the dispersion of periodic lossless LC circuits. The application of this idea is three-fold: (1) demonstrating how SED proves useful, should the analytic methods of calculating dispersion of a circuit render difficult (due to nonlinearity or having many elements), (2) teaching the concepts like Brillouin Zone, dispersion (or band structure), zone folding, gap formation and avoided crossing to students of physics and electrical engineering by highlighting the similarities of phonon and periodic circuits, and (3) studying the thermal devices, e.g., heat rectifiers using commercial circuit simulators.