Predicting Q-Day: A Fractal Mathematics Approach to Quantum Computing Timelines

Syed Muntasir Mamun

Published Dec 20, 2025• 0 citations

Abstract

This paper employs fractal mathematics principles to forecast Q-Day—the threshold at which fault-tolerant quantum computers can practically compromise public-key cryptography—over an 18-month horizon from December 2025. Synthesizing insights from recent advancements in quantum ecosystems, algorithmic hybrids for nonlinear matrix operations, and interdisciplinary frameworks integrating quantum entanglement with fractal geometries in high-dimensional computing, the analysis models technological progress as self-similar iterative processes. Utilizing iterated function systems and fractional dimensions (approximately 1.618, akin to the golden ratio), the fractal model projects accelerated convergence toward utility-scale systems, predicting Q-Day by late 2027 with a 70% probability within the specified timeframe. Key drivers include the end of the Noisy Intermediate-Scale Quantum (NISQ) era, polylogarithmic speedups in quantum algorithms, and recursive self-improvement in autopoietic multi-agent systems. Implications encompass urgent transitions to post-quantum cryptography, geopolitical divergences in investment strategies, and existential risks from quantum-AI synergies, advocating for coordinated policies in commercialization, international collaboration, and ethical regulation to mitigate vulnerabilities while harnessing transformative potential in cybersecurity, healthcare, and environmental monitoring. Also available on Academia.edu: https://www.academia.edu/attachments/125804561/download_file?s=portfolio

DOI: 10.5281/zenodo.22995709

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