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 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 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 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 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 preprint introduces Φ_struct, a graph-weighted structural functional defined on quantum channel and interaction-graph pairs. The framework is motivated by the established non-uniqueness of open quantum-system realizations, where distinct microscopic interaction architectures can generate identical Lindblad dynamics while differing at the process level. The proposed functional combines the Choi representation of a quantum channel with a graph-derived locality tensor to provide a computationally inexpensive structural diagnostic for comparing candidate interaction architectures. Formal properties are established, including invariance on fixed graph-assigned Lindblad equivalence classes and discrimination between graph-distinct implementations sharing identical reduced dynamics. An illustrative two-environment model demonstrates nonzero structural separation under equalized decoherence rates. The work does not modify quantum mechanics and does not attempt to replace process-tensor methods. Instead, it provides a graph-based organizational framework for studying interaction topology in open quantum systems. Keywords: Open Quantum Systems, Quantum Channels, Choi Matrix, Process Tensor, Decoherence, Quantum Information Theory, Non-Markovian Dynamics, Interaction Graphs.
Abstract Quantum coherence and fidelity are essential ingredients for scalable quantum technologies, particularly in solid-state platforms such as quantum dots (QDs). In this work, we introduce a physics-inspired framework for the multi-metric characterization of QDs confined to a spherical potential. We obtain the energy eigenvalues using Nikiforov-Uvarov Functional Analysis (NUFA) and calculate the thermodynamic and information-theoretic quantities of purity, Rényi-2 entropy, and dynamical loss of coherence, to give quantitative descriptors of the confinement geometry, excitation dynamics, and decoherence sensitivity. For predictive modeling, we develop a supervised deep neural network (DNN) that learns to map quantum energy features to the corresponding state metrics, providing a quick and accurate estimator that adheres to the underlying physics. Our findings indicate that the low-energy and highly localized states have the lowest entropy and highest purity, whereas the higher excited states exhibit significant decoherence and thermal leakage. This hybrid data-modeling strategy not only enables a systematic connection between the energy-level physics and quantum information-theoretic measures but also provides an enabling step towards intelligent coherence management in QD systems. The framework can be readily extended to other related near-term intermediate-scale quantum (NISQ) systems for a generalized pathway to fidelity-guided quantum design and diagnostics.