Physical Interaction Distance as a Fundamental Limit on Qubit Scaling in 2D Quantum Architectures

This work presents a simple but physically grounded model that establishes an upper bound on the number of qubits that can be effectively coupled within a two‑dimensional quantum computing architecture. While most discussions of scalability focus on gate fidelities, coherence times, or error‑correction thresholds, this study highlights a more fundamental constraint: the finite interaction distance between physical qubits. Assuming (i) a finite effective interaction range, (ii) a realistic physical footprint for each qubit including control structures, and (iii) a strictly two‑dimensional layout, the analysis shows that the maximum number of mutually interacting qubits is limited to approximately 10^2 – 10^3 . This estimate is consistent with experimental observations across multiple platforms, including superconducting qubits, semiconductor spin qubits, quantum dots, ion traps, and photonic systems. The purpose of this work is not to claim an absolute limit, but to provide a baseline, architecture‑independent reference for understanding the physical constraints that govern quantum processor scaling. By making the assumptions explicit, the model clarifies which aspects of current architectures must be changed—such as dimensionality, coupling mechanisms, or modularity—to enable scaling beyond present limits. This document may serve as a conceptual reference for researchers, engineers, and students seeking to understand the physical foundations of quantum computing scalability.