nonlinear simulations. Josephson Circuits Optimizer addresses this problem by using harmonic balance simulations in two stages: fast linear simulations to select promising circuit configurations according to properties such as impedance and phase matching, followed by nonlinear simulations to optimize their operating conditions. However, pump-induced effects such as impedance renormalization and Kerr-induced modifications of phase matching are not captured during the initial linear stage. We therefore introduce a nonlinear feedback extension that transfers information from the pumped response back to the linear optimization. The approach is investigated using a Josephson traveling-wave parametric amplifier with a reversed-Kerr architecture, whose model is validated against experimental gain measurements. We then evaluate the difference between the linear and pumped response values of a metric based on the input reflection coefficient, while excluding configurations with insufficient third-harmonic suppression. This discrepancy is considered a candidate feedback observable, as it exhibits features similar to the gain landscape, supporting its use in subsequent optimization cycles.

Josephson junctions (JJs) and other nonlinear elements within a lumped-element approach, leveraging harmonic balance, a frequency-domain technique that provides a computationally efficient alternative to traditional time-domain simulations. JCO automates the evaluation of optimal circuit parameters by implementing Bayesian optimization with Gaussian processes through a device-specific metric and identifying the optimal working point to achieve a defined performance function. This makes it well suited for circuits with strong nonlinearity and a high-dimensional set of coupled design parameters. To demonstrate its capabilities, we focus on optimizing a Josephson Traveling-Wave Parametric Amplifier (JTWPA) based on Superconducting Nonlinear Asymmetric Inductive eLements (SNAILs), operating in the three-wave mixing regime. The device consists of an array of unit cells, each containing a loop with multiple JJs, that amplifies weak quantum signals near the quantum noise limit. By integrating efficient simulation and optimization strategies, the framework supports the systematic development of superconducting circuits for a broad range of applications.