Estimating Node Capacitances of Large Transmon Networks and their Scaling Behavior

Designing large-scale transmon networks requires accurate estimation of the node capacitances — the transmon self-capacitances and coupling capacitances that determine the qubit frequencies and effective inter-qubit coupling strengths. We present a scalable framework based on multi-port admittance matrices obtained from circuit simulations, which enables quantitative extraction of node capacitances. Using this method, we systematically examine how the extracted node capacitance values emerge and evolve with circuit size and coupling topology, revealing characteristic scaling behavior beyond simple two-qubit models. The framework provides quantitative design guidelines for identifying when capacitances estimated from simple approximation no longer capture the actual circuit behavior as the network becomes more complex. Possible implications for discrepancies between the prediction of simple models and the measured inter-qubit coupling strengths are briefly discussed.