harmonic mode operators $\hat{q}_{i}=-i\sqrt{\frac{\hbar}{2Z_{i}}}(\hat{b}_{i}-\hat{b}_{i}^{\dagger})$ for the qubit modes and computing the projection of $\mathbf{C}_{q}$ onto the qubit subspace one obtains the following drive term acting in the qubit subspace

$$\begin{aligned}
H_{id}^{D} & = & i\sqrt{\frac{\hbar\omega_{i}}{2L_{i}}}\mathrm{Im}\left[Z_{i,p(d)}(\omega_{i})\right]\frac{C_{p(d)}V_{d}(\hat{b}_{i}-\hat{b}_{i}^{\dagger})}{1+i\omega_{d}Z_{0}C_{p(d)}}\label{eq:HD-id}\end{aligned}$$

from which we get

$$\varepsilon_{id}=\sqrt{\frac{\omega_{i}}{2\hbar L_{i}}}\mathrm{Im}\left[Z_{i,p(d)}(\omega_{i})\right]\frac{e^{i\theta_{d}}C_{p(d)}}{\sqrt{1+\omega_{d}^{2}Z_{0}^{2}C_{p(d)}^{2}}}\label{eq:eps-ij}$$

for the coupling matrix $\varepsilon_{id}$ appearing in the Hamiltonian in Eq. and giving the coupling of the qubit modes to the voltage drives. Here $\theta_{d}=\frac{\pi}{2}-\arctan(\omega_{d}Z_{0}C_{p(d)})$ and $Z_{i,p(d)}$ is the impedance entry connecting the qubit port $i$ to drive port(with port index $p(d)$) corresponding to the voltage source $V_{d}$. $C_{p(d)}$ is the total capacitance shunting the $d$-th drive port, $\omega_{d}$ is the frequency of the signal driving the qubit $j$ and $Z_{0}$ is the characteristic impedance of the drive lines (typically $Z_{0}=50\Omega$). The last factor in Eq. is just a voltage division factor giving how much of the drive voltage $V_{d}$ is seen across the $d$-th drive port. The factor $\mathrm{Im}\left[Z_{i,p(d)}(\omega_{i})\right]$ gives on the other hand the classical crosstalk.

\[sec:The-Classical-cross-talk\]The classical crosstalk and the location of the drive ports
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We define the classical crosstalk as the unwanted drive the qubit $i$ experiences when we excite the device only the drive line of the qubit $j$. For the purpose of 