QuLTRA: Quantum hybrid Lumped and TRansmission lines circuits Analyzer

Abstract: We present QuLTRA (Quantum hybrid Lumped and TRansmission lines circuits Analyzer), an open-source Python package for the accurate simulation of superconducting quantum circuits containing both lumped and distributed elements. QuLTRA directly models coplanar waveguide (CPW) transmission lines and multi-line couplers without discretization into lumped-element equivalents, and extracts the circuit Hamiltonian parameters using the energy participation ratio (EPR) method. This approach enables fast and accurate extraction of mode frequencies, anharmonicities, cross-Kerr interactions, and Purcell decay rates without relying on full electromagnetic simulations, while naturally accounting for higher-order modes of distributed components. The performance of QuLTRA is validated against Ansys HFSS, pyEPR, QuCAT, and results from the literature, showing excellent agreement with orders-of-magnitude reductions in computational time with respect to full electromagnetic simulations. Some application examples are discussed, including the design of Purcell filters, multi-mode ultra-strong coupling systems, and multiplexed qubit readout schemes, demonstrating that QuLTRA can efficiently simulate complex architectures relevant to circuit quantum electrodynamics applications.