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.
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.
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)
Characterizing and calibrating physical qubits is essential for maintaining the performance of quantum processors. A key challenge in this process is the presence of crosstalk that complicates the estimation of individual qubit detunings. In this work, we derive optimal strategies for estimating detuning and crosstalk parameters by optimizing Ramsey interference experiments using Fisher information and the Cramer-Rao bound. We compare several calibration protocols, including measurements of a single quadrature at multiple times and of two quadratures at a single time, for a fixed number of total measurements. Our results predict that the latter approach yields the highest precision and robustness in both cases of isolated and coupled qubits. We validate experimentally our approach using a single NV center as well as superconducting transmons. Our approach enables accurate parameter extraction with significantly fewer measurements, resulting in up to a 50% reduction in calibration time while maintaining estimation accuracy.
Abstract Several papers on physics-informed noise modeling for superconducting qubits report gains from embedding known physics into machine-learning models, but we found little discussion in that literature of the specific mechanism by which such gains arise, or of the conditions under which embedding a known relation could instead hurt. We do not claim this gap is unaddressed anywhere in the broader machine-learning literature — bias-variance behavior of physics-informed models and the importance of multi-seed evaluation are both studied elsewhere in adjacent settings, discussed in Section 2 — only that we did not find this specific mechanism characterized for noisy-input extrapolation in the quantum-noise-modeling papers we reviewed. We derive a leading-order (small-σ) bias-variance decomposition for anchoring a regression model to an exact analytic noise relation (here, the T1-relaxation-limited dephasing rate 1/(2T1)): to leading order in the relative input-noise magnitude σ, the exact plug-in estimator has a small positive relative bias of σ² and a variance scaling with the square of the anchored quantity's absolute magnitude. We validate both predictions in a controlled single-variable Monte Carlo experiment: the simulated relative bias (0.65%) matched the leading-order prediction (0.64%) closely, and the simulated variance ratio between two test points matched its prediction to within about 1%. We then test whether this single-variable picture transfers to a more realistic two-feature extrapolation task — predicting the excess, non-relaxation-limited dephasing rate of a held-out device from noisy T1/T2 telemetry — using calibration parameters grounded in five real, independently re-verified IBM Heron/Eagle/Osprey processor snapshots, including a cross-generation transfer test (training on three Heron-class devices, T1 ≈ 137–189µs, evaluating on both a lower-coherence Osprey-class device, T1 ≈ 88µs, and a higher-coherence Eagle-class device, T1 ≈ 263µs). Run once, the isolated single-variable picture does not predict the sign of the effect in this more realistic setting: physics-anchoring loses to a plain ridge baseline on the low-T1 device. Repeating the experiment across 20 independent random seeds, with a one-sample t-test against zero, shows why: the low-T1 effect is statistically indistinguishable from zero (mean − 2.5%, 95% CI [− 10.5%, + 5.4%], t(19) = − 0.67, p = 0.51, 12 of 20 seeds favoring physics-informed), while the high-T1 benefit is statistically robust (mean + 19.7%, 95% CI [+ 16.7%, + 22.7%], t(19) = 13.7, p < 0.0001, 20 of 20 seeds favoring physics-informed). A follow-up collinearity-manipulation experiment, itself repeated across 15 seeds per condition, initially appeared non-significant when analyzed by pooling all seed-condition pairs into one regression; a corrected per-seed-slope analysis, accounting for the repeated-measures structure induced by reusing seeds across jitter levels, instead finds a small but statistically significant positive trend at both held-out devices (p = 0.021 and p = 0.011). All experiments are grounded in real, independently re-verified device numbers but built from synthetic telemetry — documented in full, equation by equation, in Section 6 — in a network-isolated environment without access to live quantum hardware; results should be read as a methodological, cautionary study on synthetic data, not a validated hardware finding, and we make no claim that any of the specific numeric effect sizes would reproduce on real devices. We report this honestly, including a citation error we found and fixed in our own earlier draft and a headline finding (the low-T1 reversal) that did not survive statistical testing, because both are more useful to a careful reader than a clean story would have been. Complete reproduction code is included with this submission.
This technical report develops and tests TWMSE Candidate Equation 4A, a phenomenological, threshold-activated model of observer-induced quantum collapse formulated to preserve Born weights and operational no-signalling while producing experimentally distinguishable dynamics. Candidate Equation 4A introduces a branch-sensitive Lindblad term whose activation depends on whether an operationally defined observer record exceeds a specified threshold. The report evaluates the equation’s mathematical consistency, including trace preservation, positivity, Born-weight preservation and operational no-signalling. It also examines individual stochastic trajectories, ensemble behaviour, synthetic count-level parameter recovery, statistical power and the consequences of model misspecification. A retrospective analysis is performed using published fitted GHZ decoherence-rate summaries from two superconducting-qubit studies. This is not an analysis of original laboratory shot-level data. The combined profile analysis finds no robust positive signal for Candidate Equation 4A. Instead, it establishes provisional, threshold-dependent upper limits on the additional collapse rate. Across the report’s primary threshold range of R* = 1–9, the largest pointwise one-sided 95% upper limit is approximately 7.3 × 10³ s⁻¹, while the tightest limit is approximately 3.0 × 10³ s⁻¹ at R* = 8. These are pointwise limits and do not constitute a simultaneous confidence band. The retrospective results therefore constrain but do not favour Candidate Equation 4A. Standard quantum mechanics remains sufficient to describe the analysed GHZ summaries and does so with fewer parameters. Candidate Equation 4A survives this preliminary confrontation only in the limited scientific sense that portions of its parameter space remain unexcluded. This non-exclusion is not evidence that the candidate is correct. The report consequently specifies a dedicated amplify–hold–erase experiment using matched record-forming and coherent-control circuits. The proposed test varies observer-record size, conditional record strength and dwell time while collecting count-level measurement outcomes and contemporaneous calibrations of conventional noise. The protocol is designed to distinguish a threshold-activated observer-record contribution from smooth, conventional decoherence and other experimental effects. A preregistration template, empirical-data schema and data dictionary are supplied so that the proposed experiment can be performed and analysed as an independently reproducible and falsifiable test. The accompanying ZIP archive is the complete, self-contained reproducibility package for the results reported here. It contains the code, simulation data, published GHZ rate summaries used as inputs, derived numerical outputs, documentation, software requirements and integrity checks required to reproduce the reported computational analyses and verify the packaged results. The archive contains: • the complete report in PDF, DOCX and Markdown formats;• deterministic Python reproduction scripts;• results from 500 density-matrix consistency trials;• 250,000 simulated stochastic trajectories;• 14,336 synthetic count-level circuit rows;• synthetic parameter-recovery and statistical-power results;• model-misspecification tests;• the published fitted GHZ rate summaries used in the retrospective analysis;• individual and joint GHZ profile-likelihood results;• prediction grids and report figures;• an empty 37-column template for future empirical raw data;• a data dictionary and preregistration template;• software-environment requirements and citation metadata; and• a SHA-256 manifest for package-integrity verification. The simulated trajectories and synthetic circuit counts are computational data rather than laboratory observations. The included GHZ inputs are published fitted rate summaries and are not original experimental shot counts. No new laboratory data are included, and no empirical discovery claim is made. Successful reproduction verifies that the supplied code generates the reported mathematical checks, simulations and retrospective statistical results. It does not establish that nature follows Candidate Equation 4A, demonstrate observer-induced collapse, or show that TWMSE is empirically preferred over standard quantum mechanics. The physical ideas, TWMSE framework, research direction and scientific interpretation are those of the author. Computational assistance was used for mathematical checking, simulation, statistical analysis, document preparation and reproducibility auditing. The author directed the research and accepts responsibility for the methodology, scientific claims, interpretations and conclusions. Candidate Equation 4A should therefore be understood as an explicit, internally testable and falsifiable phenomenological candidate that has passed the reported mathematical and computational consistency checks, remains compatible with the limited published summaries examined, and now requires the proposed dedicated raw-data experiment for a meaningful empirical test.
In the companion paper (Part I), we developed an optimal-control framework to suppress intrinsic and decoherence-induced errors in controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons. Here, we extend this framework to incorporate uncertainties in coupling strength, anharmonicities, and zero-flux qubit frequencies, enabling the design of high-fidelity gates robust against noise and parameter uncertainties. We classify these uncertainties by whether they perturb the off-diagonal coupling strengths or the diagonal detunings of the Hamiltonian, and we identify distinct suppression mechanisms for each class. Coupling errors are mitigated through dynamical decoupling induced by strong detuning modulation. For a 30-ns gate, this strategy reduces the coupling error to 6.21×10−7 and tolerates coupling-strength uncertainties up to 2π×4 MHz while keeping total gate infidelity below 10−3. Detuning errors are minimized near a symmetric-detuning operating point that balances the two dominant leakage-mediated interactions. A 24-ns gate operated near this point tolerates individual uncertainties of up to 2π×5 MHz in each relevant diagonal parameter under the same infidelity threshold. We further optimize gate performance under realistic conditions where intrinsic errors, decoherence, and parameter uncertainties coexist across six representative stages of progressively improving hardware performance. The resulting stage-specific controls achieve lower infidelity and greater robustness. Together with the companion study (Part I), this framework offers a practical approach to balance speed, fidelity, and robustness while reducing the need for exhaustive characterization and frequent recalibration in large-scale superconducting quantum processors.
Classical optimization assumes a definite landscape: given a problem, the objective function f(x) exists prior to investigation, and algorithms search for its extrema. We introduce a parallel framework, the *fog landscape*, in which the optimization domain itself is observation-induced: it does not exist prior to multi-chain deployment but emerges from the deployment as a statistical structure on the chain ensemble. Each chain is a collapse chain on a domain-specific observation system (S, Ω, Φ), evolving independently under environmental influence via completely-positive trace-preserving (CPTP) maps. After T evolution steps, the ensemble is reverse-fitted to a continuous functional form using Gaussian Mixture Models (GMM). The resulting function F(x) is a legitimate NP-Hard landscape and inherits the classical NP-Hard toolkit: landscape classification, reconnaissance flattening, and algorithm selection. The framework is presented in three parts: (i) a generic specification independent of any application domain, (ii) a worked example demonstrating the framework on the NSD financial trading system with d=11 personality dimensions, and (iii) cross-domain guidance for application to quantum cognition, epidemiology, and strategic forecasting. Fog landscapes constitute a parallel ontological category to classical NP-Hard landscapes—not a reduction, generalization, or mirror correspondence, but an independent class of mathematical objects—while admitting reduction at the operational level for tool reuse. The strong-Copenhagen interpretation is essential: the fog landscape is the genuine mathematical object characterising indeterminate optimization, not an approximation to a hidden continuous truth. This is a working paper. v1 establishes the framework architecture and demonstrates feasibility on the NSD financial system. Mathematical proofs (Proposition 2), explicit Kraus operator forms for NSD, and the ontological commitment defense are abbreviated; v2 will expand these. Comments welcome. Version 2 (April 2026) — Substantial revision incorporating reviewer feedback from three independent sources and one author-reveal. Major additions and refinements: §1.2 Strong Copenhagen as logical necessity. The ontological commitment is reframed from a stylistic choice into a structural requirement, established via stress-testing against five alternative interpretations (Standard Copenhagen, Bohmian, Many-Worlds, QBism, Decoherent Histories). Each alternative is shown to fail the framework's constitutive claim or operational behavior. Operational compatibility paragraph added for readers committed to alternative interpretations. §5 Historical pre-segment and junction point. New subsection explicitly handling the chain ensemble's initial state. The multi-chain fan-out begins from an informed posterior γ_0, derived from a single historical chain over t = -N*, ..., 0. This structure mirrors MC-CBPTT's Hybrid Chain and is required by the strong-Copenhagen commitment (past observations have collapsed; multi-chain fan-out begins from the system's real, accumulated past). §3 CPTP existence anchor. Stinespring dilation and Choi–Kraus theorem cited (Nielsen & Chuang Ch. 8). Three operational requirements (trace preservation, complete positivity, linearity) made explicit. Why-CPTP-not-Monte-Carlo defense expanded across operational, mathematical, and ontological levels. §6.3 Why GMM. Comparison against KDE, neural density estimators, t-mixtures, and maximum entropy distributions. Four desirable properties of GMM articulated. Framework explicitly stated to be reduction-method neutral. §6.5 Stability and sensitivity. New subsection covering component count K, sample size N (per-parameter complexity O(d²/N)), convergence and initialisation, informal Wasserstein-2 → L² sensitivity bound (formal proof deferred to v3), and four practical recommendations. §6.6 Operational vs ontological defense. Expanded from 3 sentences to a full page. Three defenses against the "fog landscape is just elaborate density estimation" challenge: (1) deployment dependence, (2) strong-Copenhagen commitment at ensemble level (parallel to Layered Observation's α vs κ), (3) reduction as operational tool reuse (Fourier transform analogy). §7.2 Continuous-optimization scope. Honest scope-bounding: the framework inherits the continuous-optimization portion of the NP-Hard toolkit, not the entire toolkit. Tools that transfer directly, require adaptation, or require domain bridging are explicitly listed. §4.3 Path integral disambiguation. Structural parallel preserved but explicitly delimited: density matrix ensemble aggregation does not involve phase coherence or interference effects. §8.2 NSD Kraus operators. Decomposition K_k(E, ψ) = K_k^(E) · P_ψ made explicit. Eleven Digital Exhaust correction operators and six personality filters described in detail. HMM forward update written as explicit Kraus form K_1^(E) = diag(√B) · √A. Full matrix entries deferred to v3 Appendix A. Definition 2 (Chain ensemble) and Definition 3 (Fog landscape as deployment-indexed empirical measure on personality space). The fog landscape is now a measure, not a function—the function F(x) emerges only after GMM reduction. Proposition 2. Proof added (using Bishop Ch. 2). Property (4) "admits optimization tools" demoted to Remark; the proposition covers only mathematical properties of F(x). Figure 2 expanded to four panels: (A) historical chain converging to junction, (B) junction point γ_0, (C) multi-chain fan-out, (D) ensemble at t = T as fog landscape measure μ_T,C. Bibliography expanded: Nielsen & Chuang (CPTP), McLachlan & Peel (GMM theory), MOEH paper, MC-CBPTT paper, LANCER 2023 (landscape surrogate comparison). v3 substantially expands the framework's mathematical foundations and programme integration. New: formal Wasserstein-2 sensitivity theorem with full proof (Theorem 1, Appendix B); explicit Kraus operator construction for the NSD test case with Lüders-rule formalisation (Appendix A); fourth Defense identifying the GMM reduction operator as a collapse operator in the unified programme language (§6.7); consolidated notation table (Appendix C). Sharpened: §3.1 density matrix grounding now anchored in four sister papers (Layered Observation, Five-Step Methodology, MOEH, MCCO); §1.2 strong-Copenhagen position now empirically anchored via the consensus interference parameter measurement κ̂=0.3606 (p<0.001); §10 limitations expanded from 3 to 7 substantive items; §11 closing now positions the paper within the FOG-1/2/3/4 series. Two reference bugs fixed: bibkey collision between MC-CBPTT and MCCO; MOEH paper title corrected. New external citations: Pitzer 2012 (FLA) and Mersmann 2011 (ELA). Mathematical correctness fix in §8.2/Appendix A: per-personality update reframed as Lüders rule with explicit renormalisation (the v2 multiplicative form K=K^(E)·P_ψ does not preserve trace; v3 makes the renormalisation explicit, consistent with the diagonal Lüders rule of MOEH Theorem 1).