QRAFT-RA (Quadrature-based Reproducible Action-Structured Framework with Regularized Action) is a deterministic contextual variational framework for generating and verifying non-classical correlations through a fully reproducible computational pipeline. The framework combines: • a contextual action landscape on a compact latent domain• a Gibbs-type contextual distribution controlled by an inverse temperature parameter• an analytic noise-aware measurement map• deterministic quadrature evaluation of correlators and Bell-type functionals A complete deterministic verification hierarchy (V1–V17) is reported, including convergence tests, adversarial optimization under operational no-signaling constraints, industrial correlator validation (V14), and Titan-scale statistical stress testing (V15). In the General-MD regime the framework deterministically generates super-Tsirelson correlations: CHSH ≈ 3.576310390010 while maintaining operational no-signaling at machine precision: SIG ≈ 10⁻¹⁶. The work is presented as a deterministic mathematical and computational archetype for exploring contextual correlation structures and reproducible simulation pipelines. Related patent application:PCT/IB2026/050200 (QRAFT-RA-PCT-2026-01).
QRAFT-RA (Quadrature-based Reproducible Action-Structured Framework with Regularized Action) is a deterministic contextual variational framework for generating and verifying non-classical correlations through a fully reproducible computational pipeline. The framework combines: • a contextual action landscape on a compact latent domain• a Gibbs-type contextual distribution controlled by an inverse temperature parameter• an analytic noise-aware measurement map• deterministic quadrature evaluation of correlators and Bell-type functionals A complete deterministic verification hierarchy (V1–V17) is reported, including convergence tests, adversarial optimization under operational no-signaling constraints, industrial correlator validation (V14), and Titan-scale statistical stress testing (V15). In the General-MD regime the framework deterministically generates super-Tsirelson correlations: CHSH ≈ 3.576310390010 while maintaining operational no-signaling at machine precision: SIG ≈ 10⁻¹⁶. The work is presented as a deterministic mathematical and computational archetype for exploring contextual correlation structures and reproducible simulation pipelines. Related patent application:PCT/IB2026/050200 (QRAFT-RA-PCT-2026-01).
Version 6.1 presents an integral framework for an enhanced GRAPE algorithm for quantumoptimal control.The architecture combines:1. finite-dimensional Hamiltonian control;2. exact or controlled numerical propagation;3. analytic GRAPE gradients using exact Fréchet derivatives;4. gradient verification by independent numerical differentiation;5. robustness to parameter uncertainty;6. robustness to stochastic and quasistatic noise;7. amplitude and slew-rate constraints;8. spectral regularization;9. train/validation/test separation at the level of individual uncertainty realizations;10. multi-start optimization;11. computational-budget-matched comparison; 12. ablation analysis;13. distribution-shift stress testing;14. preregistered statistical analysis;15. independent reproducibility.The central optimization problem is written as a constrained robust optimization problem:maxϵJ(ϵ) (1)subject to amplitude, slew-rate, bandwidth, and numerical constraints.The robust objective is constructed from an in-sample expectation of gate or state-transferfidelity together with explicit regularization terms.A separate held-out distribution is reserved for validation and a locked test distribution isreserved for final evaluation.The framework distinguishes:training performance ̸= validation performance ̸= test performance. (2)The exact propagator derivative is expressed using the Fréchet derivative of the matrixexponential:∂Un∂ϵk,n= D expAn[︃−iℏHk∆t]︃, (3)whereAn = −iℏHn∆t. (4)This formulation avoids the mathematically invalid simplification ∂eA/∂x = eA ∂A/∂x,which only holds under additional commutation conditions.Version 6.1 additionally introduces formal computational-budget specification, ablationexperiments, paired statistical comparisons, bootstrap confidence intervals, multiple-comparisoncontrol, computational profiling, and independent reproduction.No experimental advantage is claimed.
Non-convex stochastic optimization presents fundamental mathematical challenges across machine learning, wireless networks, data center resource allocation, and optical wireless communication systems, where complex loss landscapes with multiple local minima and saddle points impede classical variational inference methods. This paper introduces the Quantum-Inspired Variational Inference (QIVI) framework, which systematically integrates quantum mechanical principles (superposition, entanglement, and measurement operators) into classical variational inference through rigorous mathematical formulations grounded in Hilbert space theory and operator algebras. We develop a unified optimization framework that encodes classical parameters as quantum-inspired states within finite-dimensional complex Hilbert spaces, employing unitary evolution operators and adaptive basis selection governed by gradient covariance eigendecomposition. The core mathematical contribution establishes that QIVI achieves a convergence rate of O(log2T/T1/2) for σ-strongly non-convex functions, provably improving upon the classical O(T−1/4) rate, yielding a theoretical speedup factor of 1.85–1.96×. Comprehensive experiments across synthetic benchmarks, Bayesian neural networks, and real-world applications in network optimization and financial portfolio management demonstrate 23–47% faster convergence, 15–35% superior objective values, and 28–46% improved uncertainty calibration. The principal contributions include: (i) a rigorous Hilbert space-based mathematical framework for quantum-inspired variational inference grounded in operator algebras, (ii) a novel hybrid quantum–classical algorithm (QIVI) with adaptive basis selection via gradient covariance eigendecomposition, (iii) formal convergence proofs establishing provable improvement over classical methods, (iv) comprehensive empirical validation across diverse problem domains relevant to machine learning and network optimization, and (v) demonstration of the framework’s applicability to optimization problems arising in wireless networks, data center resource allocation, and network system design. Statistical validation using the Friedman test (χ2=847.3, p<0.001) and post hoc Wilcoxon signed-rank tests with Holm–Bonferroni correction confirm that QIVI’s improvements over all baseline methods are statistically significant at the α=0.05 level across all benchmark categories. The framework discovers 18.1 out of 20 true modes in multimodal distributions versus 9.1 for classical methods, demonstrating the potential of quantum-inspired optimization approaches for challenging stochastic problems arising in machine learning, wireless communication, and network optimization.
This preprint presents a signal-theoretic and numerical investigation into informational coarse-graining within multiscale deterministic dynamical systems. Operationally defined by the parameter σ (the log-ratio of system frequency to observer bandwidth), the framework evaluates how effective laws emerge from band-limited, finite-resolution observation under causal memory constraints.Methodological Note: This work is the product of an aggressive, iterative process of conceptual pruning and adversarial validation. The initial hypothesis began as an ambitious, macro-scale cosmological and ontological framework attempting a fundamental derivation of quantum mechanics (Born's rule and Bell non-locality). When subjected to rigorous numerical stress tests—including high-order Fourier decomposition, non-harmonic forcing, and parameter space sweeps—the initial speculative and over-parameterized claims collapsed into trivial algebraic identities.By systematically stripping away non-universal components and resisting confirmation bias, the model converged to its current irreducible, robust core: a strictly local, phenomenological demonstration that deterministic systems with causal memory naturally project a trigonometric modulation under bandwidth-dependent noise. This paper documents the exact boundary limits where the numerical simulation stabilizes, presenting a case study of structural robustness under quantitative instability.
Repository for the manuscript "Extending Bell’s Representational Framework: Modeling the Quantum and Classical Regimes" and its supporting verification artifacts. The paper demonstrates that while Bell’s single-stage theorem is mathematically sound within its algebraic scope, a two-stage contextual extension preserves strict locality, setting independence, and operational no-signaling while accounting for Bell-violating quantum correlations up to Tsirelson’s bound. Includes the complete, machine-checked Lean 4 with Mathlib formalization package (zero sorry, standard axioms) and Python linear programming verification scripts.
This paper presents Q-INTEL, a hybrid quantum–classical architecture for noise-aware inference in distributed cyber-physical systems. It integrates classical feature processing, variational quantum circuits (VQCs), classical optimisation, and edge–cloud orchestration within a five-layer pipeline. Q-INTEL does not introduce new quantum primitives; instead, it combines established encoding, variational-circuit, parameter-shift, and optimisation methods to analyse accuracy, robustness, latency, energy, and distributed operation. Evaluation is conducted entirely through noise-calibrated classical simulation using parameters representative of IBM Eagle-class superconducting devices, with no execution on physical quantum hardware. Latency and energy are analytically modelled rather than directly measured, so energy results represent relative indicators rather than physical consumption. The framework distinguishes batch-level service latency from per-inference analytical latency and identifies metrics as simulation-derived, modelled, or architectural. A quantum key distribution (QKD) synchronisation interface is included only as an architectural component and is not experimentally evaluated. Under the stated assumptions, Q-INTEL achieves favourable accuracy, robustness, latency, and energy-index results compared with the considered CNN and QNN baselines. These findings provide preliminary evidence of architectural feasibility but do not demonstrate quantum advantage. Future work requires physical-hardware validation, stronger hybrid baselines, comprehensive statistical analysis, and testing on domain-specific distributed-sensing datasets to assess practical performance under realistic deployment conditions comprehensively.
We present a machine-checked Bell-consistency analysis for the finite-dimensional singlet sector of Constraint-Surface Dynamics (CSD), in which realised outcomes are deterministic almost everywhere and reproduce Bell-violating singlet correlations, while the finite measurement dynamics remain tensor-factorised and the observable marginals satisfy no-signalling. Given a singlet preparation sector and measurement independence, deterministic context-indexed outcome maps on a shared probability space reproduce Pst(a,b)=41−sta⋅b, and attain the maximal quantum CHSH value 22. We formally prove that no compatible setting-local four-response assignment A1,A2,B1,B2 can reproduce the singlet correlations at the four specified CHSH contexts, namely that the realised maps cannot all satisfy Fij(x)=(Ai(x),Bj(x)). The Bell obstruction therefore excludes a compatible setting-local four-response representation of the singlet correlations at the four specified CHSH contexts, not determinism of the realised outcome. The formal development also studies the structure of the finite measurement interaction in the same singlet sector, without assuming that the contextual outcome family is derived from that finite measurement dynamics. Local setting transformations UA(a)⊗UB(b) and local detector couplings VA⊗VB compose as (VA⊗VB)(UA(a)⊗UB(b))†=(VAUA(a)†)⊗(VBUB(b)†), so the complete finite measurement chain remains tensor-factorised. Pointer-volume probabilities reproduce the singlet law for all detector settings, including the perfect-correlation and perfect-anticorrelation limits. Operational no-signalling is verified at both the singlet-kernel and pointer-volume levels, with each local marginal equal to 1/2 and invariant under the remote setting. The singlet preparation sector and measurement independence are explicit assumptions, and no general no-signalling theorem for arbitrary non-factorising ontic dynamics is asserted. The contribution is not a new Bell inequality or a new general result that deterministic models can reproduce Bell-violating correlations. Rather, it is a CSD-specific consistency construction and a machine-checked separation of contextual determinism, Bell-local response factorisation, finite measurement factorisation, and operational no-signalling. Within this stated scope, the Lean 4 development provides a formally verified example in which deterministic realised outcomes almost everywhere, Bell-violating singlet correlations, tensor-factorised finite measurement dynamics, Bell-nonfactorisable joint outcomes, and operational no-signalling coexist, while any compatible Bell-local four-response assignment reproducing the singlet correlations at the four specified CHSH contexts is mathematically excluded.