Error Budgeting for Superconducting Modular Quantum Architecture Designs

Scaling quantum computing is hindered by frequency crowding, which reduces gate fidelity in densely packed qubit systems. In this talk, we consider modular superconducting quantum architectures, particularly those based on parametric couplers such as SNAILs, which link modes high-fidelity three-wave mixing based interactions while avoiding detrimental fourth-order Kerr effects, offering precise control in high-density qubit environments​ [Zhou, et al. npj Quantum Information (2023)]. However, we still must avoid frequency collisions between both intended links powering gates and a variety of other parametric couplings among the SNAIL coupler and qubit modes. To tackle the frequency allocation problem, we model separation constraints between interaction frequencies using k-coloring, defining minimum spectral distances for high-fidelity operations. Through linear programming, we solve a constrained optimization problem to allocate qubit frequencies while accounting for hardware limitations like bandwidth and fabrication precision. A combined strategy of error modeling and numerical optimization determines frequency separation thresholds to preserve gate fidelity as qubit density increases. This work provides a scalable framework for modular quantum architectures, optimizing frequency allocation to mitigate crowding effects. Future efforts will extend this approach to multi-module systems, aiming for efficient large-scale quantum computing implementations.