Quantifying the Hadamard Resilience Effect and the Coherence Gap in NISQ-Era Classifiers
Abstract
We report on a fundamental disparity between stochastic noise models and algorithmic performance in NISQ-era classifiers. Utilizing the ibm_kingston processor, we characterize the "Kingston Constant" (κ≈ 0.07), representing a 93% signal magnitude collapse. Despite this decay, we show via a hardware-calibrated stochastic digital twin that a Hadamard Test based Perceptron maintains a 93.9% accuracy for the MNIST dataset, validating our proposed Hadamard Resilience Effect under affine depolarization. Through parametric simulation, we establish a critical gate-noise threshold at λcrit ≈ 0.65 (corresponding to a critical signal retention αcrit ≈ 0.35) where topological rank preservation breaks down. Furthermore, physical execution at high feature depths (N = 256) reveals a systemic divergence---the ``Coherence Gap'' (Δρ≈ 0.91)---where physical hardware classification accuracy collapses to 53.0\% due to a ``Coherence Wall'' at a circuit depth (D ≈ 10k) exceeding the hardware's resilient depth limit (Dmax ≈ 3.5k). This gap is consistent with coherent phase errors and crosstalk being the dominant unmodeled contributors under the tested hardware configuration, establishing a predictive operational boundary for NISQ classification architectures.
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BibTeX
@misc{silva2026quantifying,
title = {{Quantifying the Hadamard Resilience Effect and the Coherence Gap in NISQ-Era Classifiers}},
author = {Wladimir Silva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.10638},
eprint = {2605.10638},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.10638},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantifying the Hadamard Resilience Effect and the Coherence Gap in NISQ-Era Classifiers
AU - Wladimir Silva
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2605.10638
UR - https://arxiv.org/abs/2605.10638
AB - We report on a fundamental disparity between stochastic noise models and algorithmic performance in NISQ-era classifiers. Utilizing the ibm_kingston processor, we characterize the "Kingston Constant" (κ≈ 0.07), representing a 93% signal magnitude collapse. Despite this decay, we show via a hardware-calibrated stochastic digital twin that a Hadamard Test based Perceptron maintains a 93.9% accuracy for the MNIST dataset, validating our proposed Hadamard Resilience Effect under affine depolarization. Through parametric simulation, we establish a critical gate-noise threshold at λ_crit ≈ 0.65 (corresponding to a critical signal retention α_crit ≈ 0.35) where topological rank preservation breaks down. Furthermore, physical execution at high feature depths (N = 256) reveals a systemic divergence---the ``Coherence Gap'' (Δρ≈ 0.91)---where physical hardware classification accuracy collapses to 53.0\% due to a ``Coherence Wall'' at a circuit depth (D ≈ 10k) exceeding the hardware's resilient depth limit (D_max ≈ 3.5k). This gap is consistent with coherent phase errors and crosstalk being the dominant unmodeled contributors under the tested hardware configuration, establishing a predictive operational boundary for NISQ classification architectures.
ER -