A Black-Box Quantum Model for Superconducting Traveling-Wave Parametric Amplifiers

Superconducting quantum computing is at the forefront of demonstrating quantum advantages for revolutionary applications in science and technology. One key component for the readout of qubit state information is given by superconducting traveling-wave parametric amplifiers (TWPAs) due to their low power dissipation and unprecedented quantum-limited noise performance. This work presents a black-box circuit quantum electrodynamic model for TWPAs with arbitrary superconducting nonlinear elements. A unified Hamiltonian description for directly pumped and flux-driven amplifiers is derived, and analytic results for the gain and the added quantum noise are presented, closely matching recent experimental realizations. We also offer an optimization strategy for nonlinear elements for large gain and low noise based on the proposed black-box quantum model. The results of this article will be helpful in the design and multitarget optimization of new and improved quantum-limited low-noise amplifiers.