Crosstalk Dispersion and Spatial Scaling in Superconducting Quantum Arrays

Residual crosstalk between non-adjacent qubits introduces correlated errors that violate the independence assumptions underlying quantum error correction, presenting a critical barrier to fault-tolerant quantum computation. We present a theoretical framework and experimental results for understanding and suppressing crosstalk in fixed-frequency transmon arrays. The model captures three mechanisms: (i) exponential spatial localization arising from the inverse of banded capacitance matrices, (ii) suppression from virtual multi-hop paths that scales with detuning to intermediate modes, and (iii) enclosure-mediated coupling in a below-cutoff environment that decays with distance. Measurements on a 4×4 device with inductive shunt pillars reveal a strong separation dependence and show that treating exchange couplings as distance-independent causes standard dispersive estimates to overpredict non-nearest-neighbor interactions. Incorporating the spatial and spectral dependencies yields quantitative agreement and provides design rules for multi-band frequency allocation and geometry-aware layout that reduce long-range interactions while preserving intended nearest-neighbor coupling, offering a practical path to crosstalk-aware scaling of superconducting quantum processors.