This technical note documents the numerical stability of a two-peak (Z-level) interference pattern observed in a fixed 29-qubit quantum circuit. The analysis was performed using the Qiskit AerSimulator backend under controlled conditions, including variations in shot count and phase-parameter offsets. The results demonstrate that the observed interference structure is reproducible, robust against sampling fluctuations, and not dependent on fine-tuned parameter choices. This document does not present a theoretical proof or physical interpretation. Its sole purpose is to provide an empirical numerical reference for the stability and reproducibility of the observed interference pattern, serving as a supporting record for related theoretical and conceptual works by the author. In version v3, the numerical analysis is extended beyond 63 qubits up to 79 qubits by employing reduced statistical descriptors rather than full state-space representations. This extension demonstrates that the observed Z-level interference stability persists under scalable statistical evaluation, without requiring exponentially growing state-vector simulations. Additional clarification The reported “Z-level progress” refers to an internal, relative coverage metric within the author’s numerical stability framework. It is not a physical completeness measure, nor a claim of global optimality. Earlier high-percentage stability values (e. g. 95–98%) correspond to local robustness indicators such as sampling consistency, seed invariance, and phase-noise tolerance within fixed parameter windows. The lower percentage reported here reflects a stricter, global aggregation across multiple independent stability dimensions. This distinction is intentional and avoids conflating local robustness with global domain coverage. This work reports a numerical stability certificate for X–Z basis statistical divergence measures obtained in controlled simulations. A multiscale grid and zoom analysis identifies a non-trivial stable phase-offset interval (pj ∈ 0. 038, 0. 052) in which total variation distance, Shannon entropy, and directed Kullback–Leibler divergences remain reproducible under changes in sampling depth, random seed, and numerical resolution. A persistent directional asymmetry between KLXZ and KLZX is numerically observed across all tested scales. This document reports numerical results only and does not claim physical realization, theoretical proof, or universal validity. Interpretational note: The absence of a direct Lorentz-covariant or gauge-field embedding should not be interpreted as a deficiency of the numerical results, but as a limitation of applying classical spacetime questions to an emergent, resonance-based stability structure. The reported Z-level behavior constrains the space of viable physical interpretations rather than completing one.
Simita Roland (Mon,) studied this question.