Crosstalk Dispersion and Spatial Scaling in Superconducting Qubit Arrays

TL;DR

This paper develops a comprehensive theoretical and experimental framework to understand and predict crosstalk in superconducting qubit arrays, revealing how spatial and spectral factors influence qubit interactions and scalability.

Contribution

The paper introduces a physics-based model that accurately predicts residual qubit couplings considering spatial decay and spectral detuning, validated by experiments on a 4x4 qubit lattice.

Findings

Exponential spatial decay of crosstalk observed

Frequency-dependent suppression matches theoretical predictions

Standard models overestimate long-range couplings without considering spatial and spectral effects

Abstract

Crosstalk between qubits fundamentally limits the scalability of quantum processors, necessitating physics-based models that can handle the complexity of large qubit arrays. Here, we develop a comprehensive theoretical and experimental framework that captures residual interactions between both adjacent and non-adjacent qubits in fixed-frequency transmon lattices. The model integrates the combined effects of exponential localization in banded capacitance matrices, suppression of virtual couplings through detuning products across intermediate modes, and evanescent decay of below-cutoff electromagnetic fields, yielding predictive scaling relations for coupling strength as a function of spatial separation and spectral detuning. Experimental characterization of a $4 \times 4$ superconducting-qubit lattice with inductive shunt pillars reveals exponential spatial decay and frequency-dependent suppression consistent with theoretical predictions, achieving quantitative agreement for all nearest-neighbor couplings across the \qtyrange[range-phrase = --, range-units = single]{4}{6}{\giga\hertz} operating range. Our results show that standard dispersive Hamiltonian approximations systematically overestimate long-range coupling when spatial and spectral dependencies are neglected; these errors propagate into circuit simulation and design strategies. Our framework provides design guidance for crosstalk mitigation in larger-scale quantum processors under realistic fabrication constraints, addressing a bottleneck in scalability.