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  • Open Access

Method for the numerical analysis of hybrid lumped-distributed superconducting quantum circuits

Simona Zaccaria* and Antonio Gnudi

  • Department of Electrical, Electronic and Information Engineering “Guglielmo Marconi”, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy and ARCES—Advanced Research Center on Electronic Systems, University of Bologna, Via Toffano 2/2, 40125 Bologna, Italy

  • *Contact author: simona.zaccaria4@unibo.it
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APS Open Sci. 1, 000088 – Published 7 August, 2026

DOI: https://doi.org/10.1103/3k95-112h

Abstract

We present a method for the numerical analysis of superconducting quantum circuits combining lumped elements, either linear or nonlinear (i.e., Josephson junctions), and distributed coplanar waveguide (CPW) structures. CPW transmission lines and multiline couplers are directly modeled without discretizing them into lumped-element equivalents, and the circuit Hamiltonian parameters are extracted by 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. We have implemented the proposed method in a Python framework, QuLTRA (Quantum hybrid Lumped and TRansmission lines circuits Analyzer), which we have used to validate the approach against full electromagnetic simulations (Ansys HFSS, pyEPR), existing circuit-analysis tools (QuCAT), and designs reported in the literature. The comparisons show excellent agreement with orders-of-magnitude reductions in computational time relative to full-wave solvers. We demonstrate applications including Purcell-protected readout, multimode ultrastrong coupling, and multiplexed qubit readout, illustrating how the method can support fast and reliable early-stage circuit design.

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APS Open Sci. 1, 000088– Published 7 August, 2026
Vol. 1
  • Received 12 February 2026
  • Revised 30 June 2026
  • Accepted 28 July 2026
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