Leveraging Growth Patterns for Quantum Computing: The Case of the (4 → 16 → 38 → 139 → …) Sequence

The paper “Leveraging Growth Patterns for Quantum Computing” argues that progress in quantum computing does not follow smooth exponential curves but instead occurs through irregular leaps. Using the sequence (4 → 16 → 48 → 139 → …) as a framework, the author suggests that breakthroughs in areas like logical qubit scaling, error correction, connectivity, coherence, and algorithms often happen when multiple innovations align, triggering step-changes in capability.

The paper develops mathematical models (recurrence relations, percolation thresholds, Bayesian change-point detection) to formalize this leap-based growth and provides case studies across superconducting, trapped-ion, and emerging topological qubit platforms. It emphasizes the need for modular architectures, milestone-driven roadmaps, and high-risk/high-reward funding strategies, since small improvements can suddenly combine to produce major advances.

Overall, the work offers a new lens for forecasting and guiding quantum computing progress, shifting attention from steady qubit counts to discrete breakthroughs that redefine the trajectory of the field.