Title: Quantum Tunneling-Aware Machine Learning: Physics-Derived Noise Models for Robust Deployment

Abstract:

As transistor dimensions shrink, they are nearing physical boundaries imposed by quantum mechanics, particularly due to electron leakage caused by quantum tunneling through ultra-thin gate oxides. While traditional digital computing systems struggle with such defects, AI inference models can remain resilient if these errors are accurately characterized. To address this, we propose Quantum Tunneling-Aware Machine Learning (QTAML). By applying the Wentzel-Kramers-Brillouin (WKB) approximation to first principles, we derive the specific distribution of weight errors that occur during deployment. Our analysis reveals structural nuances that standard Gaussian noise models fail to capture, including a precise affine mean drift, a variance hierarchy among bits led by the most-significant bit, and a layer-specific dependence on the infinity norm of weights ($|W_\ell|_\infty$) alongside the trained network’s Jacobian.

We consolidate these three structural insights into a novel algorithm called Tunneling-Aware Compensation (TAC). This method integrates closed-form mean correction with an optimal, layer-adaptive bit-budget allocation strategy based on WKB variance decomposition. In evaluations involving four convolutional architectures operating at a bit-flip probability ($p_\mathrm{flip}$) of 0.10, as well as a transformer encoder at $p_\mathrm{flip}$ of 0.05, TAC achieved 95% of the accuracy observed in clean (error-free) models. Notably, this performance was attained with 3.4 to 33.6 times less Error Correction Code (ECC) overhead compared to Uniform-MSP, a baseline approach also rooted in the same physical principles. Furthermore, a closed-form saturation ratio, denoted as $\rho^*$, accurately forecasts these performance gains. On diverse architectures, the scoring method derived from WKB theory surpasses magnitude-based allocation strategies by as much as 24 percentage points when bit budgets are limited. Crucially, this algorithm operates without requiring retraining, labeled data, or any additional overhead during inference. We also confirm the validity of the WKB-derived distributional theorems against Monte Carlo simulations. These findings bridge the gap between WKB tunneling physics and noise-resilient deep learning, offering a systematic framework for hardware-software co-design that transcends traditional scaling limitations.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC