Homotopy-Guided Adaptive Error Correction Frameworks for Fault-Tolerant Quantum Computing: A Multi-Scale Topological Approach
Murali Krishna Pasupuleti · International Journal of Academic and Industrial Research Innovations(IJAIRI) · 2025
Abstract: Quantum error correction (QEC) is fundamental to achieving fault-tolerant quantum computing. Recent advances indicate that homotopy theory and related topological methods offer powerful tools for constructing adaptive, noise-resilient error correction frameworks. By critically interpreting findings across homological and homotopical quantum error correction studies, this paper proposes a multi-scale, homotopy-guided adaptive error correction (HGAEC) framework. Statistical analysis, visual models, and scientific methods support the design. This research highlights novel pathways for topological fault tolerance, dynamic code adaptation, and resource optimization in quantum systems. Keywords: Homotopy Theory, Quantum Error Correction, Fault-Tolerant Computing, Topological Codes, Adaptive Error Correction