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
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 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.
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)
Description ΩQKD introduces a structure-sensitive operational security monitoring framework for Quantum Key Distribution (QKD) systems. Instead of relying solely on the Quantum Bit Error Rate (QBER), the proposed methodology integrates multiple normalized operational indicators—including QBER, secret key rate deficit, photon loss, timing drift, detector noise, and channel instability—into a unified mathematical security index. The framework establishes a rigorous mathematical foundation through boundedness, monotonicity, Lipschitz stability, generalized power-mean functionals, and a risk-entropy metric for distinguishing distributed degradation from structured attacks. Objective parameter weighting is performed using Shannon entropy (CRITIC-type) weighting, while alarm thresholds are determined using statistically controlled false-alarm criteria. Numerical validation based on 12,000 Monte Carlo scenarios demonstrates that ΩQKD significantly improves operational anomaly detection compared with conventional QBER-only monitoring, particularly under stealthy attack scenarios where individual indicators may remain within nominal limits. This work does not propose a new QKD protocol or a new information-theoretic security proof. Instead, it introduces a mathematically grounded operational monitoring and security evaluation methodology intended to complement existing QKD security analyses and support real-time health assessment of practical quantum communication systems.
This paper develops an engineering-facing diagnostic bridge between the recoverability-based theory of structural irreversibility and practical evaluation in quantum error correction and monitored quantum platforms. The central problem addressed in this work is that structural recoverability, threshold-like margins, false-collapse, and Recoverability Index–type diagnostics provide useful theoretical distinctions, but they do not by themselves specify how experimentalists or engineers should organize platform-level data, compare regimes, or report recoverability-relevant behavior. The paper therefore introduces a proxy map from structural quantities to engineering diagnostics. Generalized recoverability is associated with recovery performance, decoder-assisted restoration, logical-state fidelity, and related reconstruction-sensitive quantities. Threshold-like margins are associated with entropy-like, noise-sensitive, or transition-localizing proxies. False-collapse is associated with mismatch windows in which collapse-like or transition-like indicators become strong while recovery-sensitive records still indicate residual recoverability. The paper also proposes a minimal diagnostic architecture for QEC and monitored platforms. This architecture consists of four layers: an appearance-sensitive proxy, a recoverability-sensitive proxy, a threshold-like locator, and a window-based reporting layer. Together, these layers support regime classification, early-warning detection, false-collapse-like mismatch identification, finite-window reporting, and cross-regime comparison. A QEC-oriented realization is presented to show how syndrome histories, logical-failure markers, logical recovery performance, entropy-like proxies, false-collapse window frequencies, and RI-like summaries can be organized into a coherent diagnostic workflow. The goal is not to replace detailed decoder analysis or hardware-specific benchmarking, but to provide a bridge-level language for deciding what should be logged, estimated, compared, and reported when studying the approach to effective irreversibility in error-managed quantum systems. This work should be read as an engineering and experimental companion to the broader recoverability program. Its contribution is to make structural irreversibility operationally legible by mapping theoretical quantities to measurable, computable, and reportable diagnostics in contemporary quantum platforms.
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 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.