QuLTRA: Quantum hybrid Lumped and TRansmission lines circuits Analyzer

We present QuLTRA (Quantum hybrid Lumped and TRansmission lines circuits Analyzer), an open-source Python package for fast and accurate simulation of superconducting quantum circuits combining lumped and distributed elements. Unlike existing tools that discretize transmission lines into LC sections or rely on full 3D electromagnetic solvers, QuLTRA directly models coplanar waveguide (CPW) resonators and couplers through analytic admittance matrices and extracts Hamiltonian parameters via the energy participation ratio method. This approach enables rapid determination of mode frequencies, anharmonicities, cross-Kerr interactions, and Purcell decay rates with orders-of-magnitude reductions in computational cost while retaining excellent agreement with Ansys HFSS and pyEPR. We demonstrate QuLTRA’s capability through applications including Purcell-protected readout, multimode ultra-strong coupling, and multiplexed qubit readout, showing that it provides an efficient and extensible framework for circuit QED design and analysis.