AHDT-Ω/QC v1.0 introduces an Adaptive Hamiltonian Digital Twin framework for Quantum Processor Coherence Monitoring, investigating symplectic Hamiltonian energy-space divergence as a potential pre-decoherence structural indicator for near-term quantum hardware. Quantum processors are highly sensitive to microscopic disturbances. Current quantum hardware monitoring primarily relies on observable performance indicators such as: • gate fidelity degradation• error rates• calibration drift• T1/T2 relaxation measurements However, quantum state degradation may begin at the underlying Hamiltonian dynamics level before these effects become visible in computational performance. AHDT-Ω/QC explores a complementary structure-sensitive approach: Instead of only asking: “Has the quantum gate performance degraded?” it investigates: “Is the underlying Hamiltonian energy structure of the quantum processor beginning to drift?” The framework introduces: • Quantum Hamiltonian Digital Twin formulation: ℋ_quantum(t)=T(q,p)+V(q,p)+E_coh(t) where: T(q,p) represents kinetic/symplectic components, V(q,p) represents potential interaction terms, E_coh(t) represents coherence-related structural energy information. • Dual Hamiltonian Digital Twin architecture: ℋ_R(t) ↔ ℋ_D(t) (real quantum system vs digital twin reference) • Hamiltonian structural divergence metric: ΔH_F(t)=||ℋ_R(t) − ℋ_D(t)||_F • Quantum Structural Coherence Score: Ω_H(t)=exp(−αΔH_F(t)) • Logarithmic Geometric Correction (LGC) robustness layer • HAD-Ω/QC quantum anomaly monitoring pipeline • Lyapunov-based stability analysis • Uniform Ultimate Boundedness (UUB) formulation under bounded quantum noise disturbances A proof-of-concept Monte Carlo simulation study (N = 1,000) evaluates the framework using synthetic T1/T2 decoherence and Hamiltonian drift scenarios. The study investigates whether Hamiltonian energy-space divergence can provide an additional early-warning signal before measurable quantum performance degradation occurs. Included components: ✓ Symplectic Hamiltonian modeling approach ✓ Quantum energy-structure monitoring framework ✓ Coherence drift analysis ✓ Ω-based structural scoring ✓ LGC robustness mechanism ✓ Stability analysis ✓ Monte Carlo validation framework ✓ Future real-hardware validation roadmap Potential future validation targets include: • IBM Quantum hardware calibration datasets • Superconducting qubit systems • Trapped-ion quantum processors • Multi-qubit coherence monitoring environments Important note: Current quantitative results are based on synthetic proof-of-concept simulations and should not be interpreted as universal quantum error prediction guarantees. Experimental validation on real quantum processors is required as the next research phase. The long-term objective of AHDT-Ω/QC is to investigate whether Hamiltonian structural monitoring can become an additional physics-aware intelligence layer for future quantum computing reliability, calibration, and error mitigation systems. Application domains: Quantum computing, quantum hardware monitoring, quantum error mitigation, digital twins, physics-informed AI, structural intelligence, and complex system stability analysis.
AHDT-Ω/QC v1.0 introduces an Adaptive Hamiltonian Digital Twin framework for Quantum Processor Coherence Monitoring, investigating symplectic Hamiltonian energy-space divergence as a potential pre-decoherence structural indicator for near-term quantum hardware. Quantum processors are highly sensitive to microscopic disturbances. Current quantum hardware monitoring primarily relies on observable performance indicators such as: • gate fidelity degradation• error rates• calibration drift• T1/T2 relaxation measurements However, quantum state degradation may begin at the underlying Hamiltonian dynamics level before these effects become visible in computational performance. AHDT-Ω/QC explores a complementary structure-sensitive approach: Instead of only asking: “Has the quantum gate performance degraded?” it investigates: “Is the underlying Hamiltonian energy structure of the quantum processor beginning to drift?” The framework introduces: • Quantum Hamiltonian Digital Twin formulation: ℋ_quantum(t)=T(q,p)+V(q,p)+E_coh(t) where: T(q,p) represents kinetic/symplectic components, V(q,p) represents potential interaction terms, E_coh(t) represents coherence-related structural energy information. • Dual Hamiltonian Digital Twin architecture: ℋ_R(t) ↔ ℋ_D(t) (real quantum system vs digital twin reference) • Hamiltonian structural divergence metric: ΔH_F(t)=||ℋ_R(t) − ℋ_D(t)||_F • Quantum Structural Coherence Score: Ω_H(t)=exp(−αΔH_F(t)) • Logarithmic Geometric Correction (LGC) robustness layer • HAD-Ω/QC quantum anomaly monitoring pipeline • Lyapunov-based stability analysis • Uniform Ultimate Boundedness (UUB) formulation under bounded quantum noise disturbances A proof-of-concept Monte Carlo simulation study (N = 1,000) evaluates the framework using synthetic T1/T2 decoherence and Hamiltonian drift scenarios. The study investigates whether Hamiltonian energy-space divergence can provide an additional early-warning signal before measurable quantum performance degradation occurs. Included components: ✓ Symplectic Hamiltonian modeling approach ✓ Quantum energy-structure monitoring framework ✓ Coherence drift analysis ✓ Ω-based structural scoring ✓ LGC robustness mechanism ✓ Stability analysis ✓ Monte Carlo validation framework ✓ Future real-hardware validation roadmap Potential future validation targets include: • IBM Quantum hardware calibration datasets • Superconducting qubit systems • Trapped-ion quantum processors • Multi-qubit coherence monitoring environments Important note: Current quantitative results are based on synthetic proof-of-concept simulations and should not be interpreted as universal quantum error prediction guarantees. Experimental validation on real quantum processors is required as the next research phase. The long-term objective of AHDT-Ω/QC is to investigate whether Hamiltonian structural monitoring can become an additional physics-aware intelligence layer for future quantum computing reliability, calibration, and error mitigation systems. Application domains: Quantum computing, quantum hardware monitoring, quantum error mitigation, digital twins, physics-informed AI, structural intelligence, and complex system stability analysis.
Digital twin technology -- the creation of a continuously updated virtual replica of a physical system synchronised with real-time sensor data -- has transformed performance analysis in aerospace, manufacturing, and energy sectors. Applying digital twin principles to quantum hardware offers a compelling paradigm: a quantum processor digital twin (QPDT) continuously ingests calibration data (T1/T2 times, gate error rates, crosstalk coefficients) and maintains an up-to-date computational noise model that accurately predicts circuit-level performance without running circuits on physical hardware. This paper proposes the Quantum Processor Digital Twin (QPDT) framework, a systematic methodology for constructing, calibrating, and validating digital twins for superconducting and trapped-ion quantum processors. QPDT is evaluated on 18 real quantum processors across IBM Quantum, Google Sycamore, and IonQ Aria platforms over a 90-day continuous operation period. Key results: QPDT achieves circuit fidelity prediction accuracy of 96.2% (mean absolute error 0.038 across 2,400 test circuits); twin synchronisation latency of 4.2 minutes from calibration update to model refresh; and a Quantum Twin Fidelity Score (QTFS) of 0.912. QPDT reduces hardware access requirements for algorithm benchmarking by 68% while maintaining prediction accuracy within 4% of physical execution.
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 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.
Abstract Current quantum processor monitoring relies on individual qubit metrics (T1, T2, gate fidelity, readout error), missing degradation encoded in qubit-qubit relationships. Here we apply Weighted Jaccard (WJ) similarity analysis to track correlation architecture reorganization across three IBM quantum processors (ibm_fez, ibm_torino, ibm_marrakesh; 133–156 qubits each) over 30 days of calibration data. Full pairwise qubit correlation matrices are computed at each calibration snapshot and compared between temporal windows. All three backends show statistically significant architecture reorganization (WJ = 0.968–0.974, p < 0.001, permutation test, FDR-corrected; 95% bootstrap CI width < 0.012). The qubits participating most in correlation architecture reorganization show no association with conventional degradation indicators (rho = -0.051, p = 0.530), indicating that WJ detects a class of hardware change invisible to component-level monitoring. Cross-backend comparison reveals that architectural divergence between processors (~ 8–9%) exceeds within-processor temporal drift (~ 3%), suggesting hardware-specific correlation signatures.
Quantum Parameter Inference under Frequency-Structured Uncertainty: Digital Twin Validation of a Polynomial Noise Framework This project develops and validates a framework for estimating decoherence parameters in superconducting transmon qubits by exploiting polynomial frequency structure in noise. Core hypothesis: When decoherence follows Γ(ω) = κ̄ω⁴ + γ̄ω² + Γ₀, multi-frequency Ramsey measurements preserve parameter identifiability via frequency-space orthogonality (ω⁴ vs ω² sensitivity separation). Version history: - v1.0 (Dec 2025): Conceptual proposal and analogy from mechanophotonic inverse problems. - v2.0 (Jan 2026): Mathematical foundations — Lindblad derivation, explicit QFI calculation, dimensional consistency verification. - v3.0 (Mar 2026): Complete validation — analytical proofs (FIM non-singularity, D-optimal allocation, SLD commutativity), digital twin simulator with four independent noise channels, and four-method head-to-head comparison over 100 Monte Carlo trials. Key results (v3.0): - Lemma 1: det(FIM) > 0 for any two distinct measurement frequencies (proved via Lagrange identity). - Theorem 1: D-optimal design concentrates ~92% of measurements at the highest frequency. - Theorem 2: [L_κ̄, L_γ̄] = 0 — standard σ_x measurement saturates the quantum Cramér-Rao bound without entangled probes. - Digital twin confirms polynomial fit with 0.62% RMSE; discovers physically meaningful negative γ̄ from competing noise mechanisms. - Frequency-domain method achieves lowest estimation bias (0.3–0.4%) with suggestive 7% variance reduction over standard Ramsey. Limitations (honestly stated): - All validation is simulation-based (no hardware experiments). - 7% variance reduction is not statistically conclusive at 100 trials. - Single-qubit, single-codebase; independent replication needed. All code (Python) for the digital twin simulator, four estimation methods, and Monte Carlo comparison is included in this project. Key results (v3.0): - Lemma 1: det(FIM) > 0 for any two distinct measurement frequencies (proved via Lagrange identity). - Theorem 1: D-optimal design concentrates ~92% of measurements at the highest frequency. - Theorem 2: [L_κ̄, L_γ̄] = 0 — standard σ_x measurement saturates the quantum Cramér-Rao bound without entangled probes. - Digital twin confirms polynomial fit with 0.62% RMSE; discovers physically meaningful negative γ̄ from competing noise mechanisms. - Frequency-domain method achieves lowest estimation bias (0.3–0.4%) with suggestive 7% variance reduction over standard Ramsey. Limitations (honestly stated): - All validation is simulation-based (no hardware experiments). - 7% variance reduction is not statistically conclusive at 100 trials. - Single-qubit, single-codebase; independent replication needed. All code (Python) for the digital twin simulator, four estimation methods, and Monte Carlo comparison is included in this project. Author: Min Soeg Choi (ydchoi72@gmail.com) Affiliation: Independent Researcher License: CC BY 4.0 AI Disclosure: Claude (Anthropic) was used as a computational tool for derivation checking, code generation, and manuscript drafting. Core research questions, conceptual framework, and editorial decisions were made by the author.