Structure-Sensitive Quantum Networks: A Geometric Consistency Framework for Entanglement Stability and Quantum Internet Reliability — Reproducibility Package v3.0
This repository contains the full reproducibility package for: "Structure-Sensitive Quantum Networks: A Geometric Consistency Framework for Entanglement Stability and Quantum Internet Reliability" This work investigates a structure-sensitive approach for monitoring quantum network stability beyond conventional fidelity-only metrics. The proposed Ω_QN functional combines: • quantum state fidelity loss• geometric drift based on Bures distance• normalized entropy contribution to evaluate structural degradation in noisy quantum links. The package includes: • Python Monte Carlo simulation framework• quantum noise models using Kraus channels• Ω_QN early-warning analysis• preventive entanglement purification model• reproducible datasets• figure generation scripts• statistical validation workflow Version 3.0 includes reproducibility improvements: ✓ corrected Bures distance implementation✓ explicit Kraus-channel noise modelling✓ purification-based preventive correction mechanism✓ clean CSV outputs✓ fixed random seed configuration for reproducibility All reported numerical results should be regenerated from the released source code before citation. This release is a computational simulation and theoretical research framework. Physical quantum hardware validation remains future work. Part of:Structure-Sensitive Science Research Program (2026–2035) Author:Halil ÖzbilIndependent ResearcherElazığ, Turkey License:Creative Commons Attribution 4.0 International (CC BY 4.0)
This repository contains the full reproducibility package for: "Structure-Sensitive Quantum Networks: A Geometric Consistency Framework for Entanglement Stability and Quantum Internet Reliability" This work investigates a structure-sensitive approach for monitoring quantum network stability beyond conventional fidelity-only metrics. The proposed Ω_QN functional combines: • quantum state fidelity loss• geometric drift based on Bures distance• normalized entropy contribution to evaluate structural degradation in noisy quantum links. The package includes: • Python Monte Carlo simulation framework• quantum noise models using Kraus channels• Ω_QN early-warning analysis• preventive entanglement purification model• reproducible datasets• figure generation scripts• statistical validation workflow Version 3.0 includes reproducibility improvements: ✓ corrected Bures distance implementation✓ explicit Kraus-channel noise modelling✓ purification-based preventive correction mechanism✓ clean CSV outputs✓ fixed random seed configuration for reproducibility All reported numerical results should be regenerated from the released source code before citation. This release is a computational simulation and theoretical research framework. Physical quantum hardware validation remains future work. Part of:Structure-Sensitive Science Research Program (2026–2035) Author:Halil ÖzbilIndependent ResearcherElazığ, Turkey License:Creative Commons Attribution 4.0 International (CC BY 4.0)
ΩQ introduces a structure-sensitive framework for monitoring quantum system stability based on Heisenberg-picture dynamics and commutator-norm analysis. The framework defines ΩQ as a structural stability metric derived from the relationship between a Hamiltonian and observable operators, and extends it to open quantum systems (ΩQE) by incorporating environmental noise contributions. This work investigates whether structural changes in quantum systems can provide an early-warning diagnostic signal before conventional error indicators become observable. Key components include: • A commutator-norm-based structural metric derived from Heisenberg dynamics• Extension to open quantum systems with environmental interaction terms• Analytical relationship studies with fidelity and purity degradation• Robustness evaluation through parameter testing• Quantum Error Correction (QEC) benchmarks using stabilizer-based models• Surface-code-type analysis with realistic syndrome extraction timing• Proposed Stim + MWPM decoder-level validation protocol ΩQ is not proposed as a replacement for existing quantum error correction methods or as a new physical law. Instead, it is presented as a complementary diagnostic layer for studying structural transitions, degradation dynamics, and potential early-warning mechanisms in quantum systems. The framework is designed to be falsifiable and further validated through full circuit-level quantum simulations. Version: ΩQ v1.4Author: Halil Özbil
This technical report introduces the Quantum Structural-Process Functional (QSPF), a proposed complementary diagnostic framework for analyzing structural information degradation in open quantum systems. While conventional quantum metrics such as fidelity, trace distance, and Bures distance quantify state similarity, they may assign similar values to quantum processes that damage different structural components of the density matrix. QSPF introduces a structure-sensitive decomposition based on: • coherence loss• population-geometry loss• purity degradation combined into a unified functional ΩQ(t). The work presents the Structural Degeneracy Separation Principle, demonstrating that equivalent fidelity loss does not necessarily imply equivalent geometric deformation. The framework is evaluated through: • fidelity-matched single-qubit noise channels• robustness testing across initial states• Bell-state entanglement extension• comparison with trace and Bures distances• weight sensitivity analysis• additional quantum noise channels• IBM-inspired T1/T2 decoherence simulations QSPF is proposed as a complementary diagnostic tool for NISQ-era quantum processor characterization and structure-sensitive quantum control. This work is part of the Structure-Sensitive Science Research Initiative.
This work presents the fifth and final paper of the Structure-Sensitive Mathematics (SSM) research series, extending the Omega framework from mathematical foundations into physical modeling, quantum information, artificial intelligence systems, and reliability analysis. Building upon: Part I — Omega-Sensitive Function Spaces Part II — Omega-Banach and Omega-Hilbert Structures Part III — Omega-Operator Theory and Omega-Calculus Part IV — Omega-Topology and Omega-Geometry this study explores the application layer of Structure-Sensitive Mathematics. The central principle investigated is: Observable equivalence does not necessarily imply structural equivalence. The framework extends system representation from: x toward: (x, Ω(x)) where Ω represents a structure-sensitive functional combining geometric, informational, and complexity-related components. This paper introduces and discusses: • Omega-based physical field extensions • Structure-sensitive action principles • Omega-field equations • Quantum structural state discrimination • Connections with Quantum Structural Perturbation Framework (QSPF) • Structural decoherence indicators • AI model structural monitoring • Omega-based pre-failure detection • Structure-sensitive digital twin concepts Core formulations include: δ(S + λΩ) = 0 and: Ω = αG + βI + γC The proposed approach investigates whether systems that appear identical under classical measurements may contain hidden structural differences affecting future evolution, robustness, or reliability. Potential research connections include: • theoretical physics • quantum information science • artificial intelligence safety and reliability • complex adaptive systems • digital twins • predictive maintenance • structure-aware engineering systems This work does not replace existing physical, quantum, or computational theories. Instead, it proposes an additional structural analysis layer and defines open problems requiring experimental validation, domain-specific calibration, and empirical testing. Part V of V — Applications and Future Directions of Omega-Based Structural Analysis.
This repository accompanies the preprint “Mapping the Limits of Architecture-Sensitive Noise Fingerprints in Quantum States.” The work investigates when and why simple classical measurement statistics obtained from noisy quantum systems retain information about the underlying quantum state architecture, and when such information collapses entirely. Building on earlier results demonstrating the existence of architecture-dependent classical fingerprints for stabilizer states under local noise, this study systematically maps the boundaries and failure modes of that phenomenon. Using exact probability distributions for small-to-moderate system sizes, we introduce controlled departures from stabilizer structure and track the degradation of classical features under dephasing and depolarizing noise. The analysis reveals sharply conditional survival of architecture sensitivity, a consistent feature-dependent collapse ordering, and a strong dependence on measurement basis and perturbation geometry. In particular, regimes of genuine diagnostic blindness are identified, where classical statistics become architecture-indistinguishable even though the underlying quantum states remain highly structured. The archive includes the full manuscript (PDF and LaTeX source), all figures appearing in the paper, the scripts required to reproduce the numerical experiments and figures, and the corresponding data outputs. All results are based on exact numerical evaluation (no sampling, optimisation, tomography, or machine learning). The work is intended as a lightweight, diagnostic limits study, providing practical guidance on when simple classical measurements are informative and when their use is fundamentally unreliable. Together with the companion papers in this series, the repository contributes to a coherent empirical and theoretical programme on the classical observability of quantum structure under noise.Version 1.1 notes.This revision clarifies the collapse criterion used to define architecture indistinguishability, explicitly specifies numerical precision and robustness checks, and adds a qualitative reliability chart summarising when different classical features remain informative. The presentation of noise-model dependence, system-size stability, and perturbation geometry has been sharpened, and the relationship to companion papers in the series has been made explicit. No new phenomena are introduced; the update improves transparency, interpretability, and practical usability of the results.
This archive accompanies the paper Architecture-Sensitive Noise Fingerprints in Classical Statistics of Quantum States. It contains the full manuscript, all figures appearing in the paper, and the Python scripts used to generate the numerical results. The project demonstrates that classical measurement statistics obtained from noisy quantum states retain reproducible, architecture-dependent structure. Even under standard local, Markovian noise models, simple low-order classical features—such as entropy, maximum probability, parity mass, and Hamming-weight distributions—encode diagnostic fingerprints of the underlying quantum state architecture. The analysis focuses on stabilizer states (including GHZ, cluster, and star graph states), fixed measurement bases, and exact probability distributions. No machine learning, optimisation, tomography, or state reconstruction is used. All results are generated using transparent, reproducible numerical simulations. The contents of this archive are: LaTeX source and compiled PDF of the manuscript All figures used in the paper (PDF/PNG) Python scripts for generating the figures and classical feature data A README describing structure and reproducibility This archive is intended to support transparency, reproducibility, and reuse of the results, and may serve as a lightweight reference for diagnostic approaches to quantum noise and state architecture.
This work introduces ΩQ-SILQ, a structure-sensitive quantum compilation framework that extends high-level quantum programming concepts with Hamiltonian-aware stability analysis. Modern quantum compilers and languages such as Silq improve quantum software development through abstraction, resource optimization, and automatic uncomputation. However, traditional optimization primarily focuses on computational metrics such as gate count, circuit depth, and qubit usage. ΩQ-SILQ proposes an additional structure-sensitive layer based on a commutator-norm metric: Omega_Q(U,H) = ||[H,U]|| / ||U|| to evaluate the compatibility between quantum operations and the underlying Hamiltonian dynamics of the target system. The framework introduces: • Hamiltonian-aware structural scoring of quantum circuits • Structure-sensitive compiler decision functions • Integration concept with high-level quantum language pipelines • Fidelity-based validation using logically equivalent circuit decompositions • Extended GHZ benchmark experiments • A proposed Qiskit transpiler comparison protocol Initial simulations demonstrate that lower ΩQ circuit selections can preserve higher fidelity under structurally coupled noise models. A multi-sample GHZ benchmark further evaluates the relationship between structural-score differences and fidelity behavior. This work does not propose replacing existing quantum compilers or quantum error correction methods. Instead, ΩQ-SILQ is presented as a complementary pre-error structural optimization layer designed to explore how future quantum compilers may incorporate physical system dynamics alongside computational efficiency. Version v1.1 includes extended hub-selection benchmarking, and the accompanying v1.2 protocol defines future validation against Qiskit transpiler optimization levels and standard quantum algorithm families.