Precision Tests of Born-Rule Statistics on Superconducting Quantum Processors: Data, Code, and Diagnostic Analysis

Description This repository contains the complete reproducible research package accompanying the manuscript “Born-Rule Deviations Tested on Quantum Processors” and its associated Supplementary Information and Technical Note. The work develops and implements an operational framework to test the robustness of Born-rule measurement statistics on contemporary superconducting quantum hardware. The central idea is to interpret the Born rule as an equilibrium fixed point associated with modular (KMS) balance, and to quantify how controlled nonequilibrium conditions or instrumental effects may produce systematic biases in large-statistics measurement data. Importantly, no violation of quantum mechanics or of the Born rule is claimed. All observed deviations are interpreted conservatively as either instrumental noise or as upper bounds on admissible nonequilibrium effects. The repository is designed to ensure transparency, reproducibility, and clarity in the interpretation of precision quantum measurement data. Contents of the Repository The repository includes four tightly integrated components: 1. Main Manuscript Born_final.pdfThe primary research article presenting: The modular/KMS framework for interpreting Born probabilities as an equilibrium condition. A universal, normalization-preserving exponential reweighting of Born probabilities under modular imbalance. A microscopic realization using standard von Neumann premeasurement and GKLS dynamics. Locality and no-signalling consistency proofs. Experimental results on IBM Quantum superconducting processors (Bell and GHZ experiments). A precision-measurement perspective emphasizing shot-scaling, noise envelopes, and conservative interpretation. 2. Supplementary Information Born_finalsup.pdfExtended technical material including: Formal derivation and uniqueness of the modular exponential rule. Perturbative expansion and validity regime. Statistical inference framework (likelihoods, Fisher information, AIC/BIC). Explicit noise and systematic-error models for superconducting qubits. Tomographic extraction of modular imbalance. Bayesian discrimination between Born+noise and modular models. Locality and no-signalling analysis. Detailed experimental metadata and Qiskit Runtime implementation notes. 3. Technical Note / Diagnostic Appendix A standalone technical appendix consolidating diagnostic figures used to interpret the data without over-claiming: Asymmetry vs. shot number demonstrating saturation and the absence of N^{-1/2} decay, identifying systematic bias. Backend-dependent asymmetry showing device-specific variation, disfavoring universal physical effects. Born-plus-noise envelope with modular bounds, translating residual probability deviations into conservative bounds on modular imbalance via|\delta K_{000} - \delta K_{111}| \lesssim 4\,\delta p.These figures are reproduced from the main analysis for interpretational completeness and are explicitly not new experimental results. 4. Reproducible Analysis Code and Data Fully documented Python/Qiskit scripts to: Retrieve and parse archived IBM Quantum Runtime job outputs. Compute outcome probabilities, asymmetries, and shot-scaling diagnostics. Generate all figures appearing in the manuscript, Supplementary Information, and Technical Note. A minimal README explaining: Software dependencies. Execution order. Expected outputs. All plots are generated directly from raw measurement counts, without data smoothing or post-selection beyond what is explicitly documented. Scientific Scope and Interpretation This repository is intended as a precision-measurement reference, not as a claim of Born-rule violation. Its primary contributions are methodological: Demonstrating how large-N statistics can distinguish statistical fluctuations from systematic instrumental bias. Providing a framework to translate residual deviations into quantitative upper bounds on nonequilibrium parameters. Ensuring strict compatibility with locality, no-signalling, and orthodox quantum mechanics. Offering a transparent benchmark for future experiments that aim to engineer controlled non-KMS measurement regimes. All conclusions are deliberately conservative. Current datasets are shown to be fully compatible with calibrated Born-plus-noise models, and the modular framework is used exclusively to parameterize and bound possible deviations within experimentally established noise envelopes. Reproducibility and Reuse The repository is released to enable: Independent reproduction of all figures and numerical results. Cross-backend comparison using identical analysis pipelines. Extension to future hardware platforms or controlled nonequilibrium protocols. No proprietary calibration data are required. All analyses rely solely on publicly accessible measurement outputs and documented reconstruction procedures. Recommended Citation If you use this repository, please cite: Christian Balfagón, Born-Rule Deviations Tested on Quantum Processors, and associated Supplementary Information and Technical Note, Zenodo (year), DOI: [Zenodo DOI] Keywords (Zenodo) Quantum measurement Born rule Modular theory KMS equilibrium Quantum thermodynamics Superconducting qubits IBM Quantum GHZ states Bell states Precision tests Nonequilibrium quantum systems Related Identifiers Preprint / journal submission: Born-Rule Deviations Tested on Quantum Processors Supplementary Information: included in this record Technical Note: included in this record