What Is the Maximum Density of Microwave Control Lines in a Superconducting Quantum Computer?

Scaling up superconducting quantum computers requires denser control wiring, introducing microwave crosstalk along the entire cryogenic signal path rather than only near the chip. Here, we introduce a framework that combines microwave transmission-line theory with a quantum Hamiltonian description to quantify the wiring-induced microwave crosstalk and the resulting gate infidelity for an all-microwave universal gate set. Using this approach, we determine the equal-level far-end crosstalk (ELFEXT) required to operate fixed-frequency transmons at arbitrary target fidelities and find that achieving 99.99% fidelity requires ELFEXT levels of approximately -43  dB for the R_{X} gate and -73  dB for the cross-resonance gate. Finally, we use these results to bound the number of physical qubits on a chip.