Entropy-Induced Collapse (EIC) Model – Part (2) Refining the Entropy-Induced Collapse (EIC) Model for Quantum Computing: Large-Scale Quantum Error Correction, Non-Markovian Noise, and Experimental Validation

This paper presents Part (2) of the Entropy-Induced Collapse (EIC) Model series, significantly refining the theoretical framework introduced in Part (1). The EIC model is a deterministic-stochastic theory describing quantum wavefunction collapse as triggered when the environmental entropy S_{\mathrm{env}}(t) surpasses a dynamically evolving critical threshold S_{\mathrm{crit}}(t). In this work, we explicitly integrate large-scale Quantum Error Correction (QEC), realistic non-Markovian fractional Brownian motion (fBm) noise, and detailed numerical validations via high-performance computing (HPC) simulations. We rigorously derive and empirically validate an analytical expression for the critical entropy threshold shift \delta(d), showing a logarithmic dependence on the QEC code distance d: \delta(d) = A_{\mathrm{QEC}}\ln d + B_{\mathrm{QEC}}, with parameters precisely determined from extensive simulations: A_{\mathrm{QEC}} = 0.232 \pm 0.052\,k_B and B_{\mathrm{QEC}} = -0.175 \pm 0.10\,k_B. Our refined model accurately predicts coherence extensions of up to approximately 80\,\mu s at code distances d \leq 11, aligning closely with experimental data from state-of-the-art superconducting quantum processors. Moreover, we quantify the detrimental impact of non-Markovian fBm noise on Quantum Key Distribution (QKD) protocols, demonstrating that increasing the Hurst exponent H from 0.5 (white noise) to 0.7 (correlated noise) elevates the Quantum Bit Error Rate (QBER) by approximately 15% and reduces the secure key generation rate by 10–12%, in excellent agreement with experimental results from ID Quantique and the Micius satellite. All numerical data, simulation codes, and detailed parameters are available upon request via our dedicated GitHub repository, ensuring reproducibility and facilitating future experimental validation and advancement in quantum information technologies. Note for LaTeX Users: This manuscript was originally written in a Japanese text environment, resulting in Yen symbols (¥) in place of standard LaTeX backslashes (). Users intending to compile or use the equations should replace all instances of ‘¥’ with ‘\’ to properly format LaTeX mathematical expressions. Important clarification regarding previous publications: All previous papers in this series (including the paper dated March 8, 2025) were unintentionally reduced by more than half of their original content due to automated AI summarization. Users are advised to refer to this current manuscript as the authoritative and complete version of the EIC model. Ethical Statement: This research is explicitly intended for peaceful purposes and should be used exclusively for the benefit of humanity.