QCDEQ V1.5: From the Brachistochrone to Quantum Rendezvous 中文:从最速降线到量子偶遇——华罗庚优选法的量子推广与波函数相遇统一框架 Trusted Timestamp:TSA-01-20260302479511973 Author: Jiang Wenjia Independent Researcher, Shenzhen, China ORCID: 0009-0000-3850-7286 Correspondence: jiangwenjiaszx@outlook.com QCDEQ Permanent Charter: TSA-01-20260225423587571 Keywords: QCDEQ V1.5; quantum brachistochrone; quantum rendezvous; wavefunction encounter; potential field orchestration; QPCTT-CW; QCENHE-LEX; QGCVT-10; quantum natural evolution; weak measurement; hospitality paradigm ABSTRACT Traditional quantum approaches chase the wavefunction: projective measurement, strong pulses, active control. They inevitably induce collapse, decoherence, and state disturbance. QCDEQ V1.5 proposes a different philosophy: instead of chasing, we orchestrate a rendezvous. The quantum is not prey to be caught, but a guest to be welcomed. This framework unifies the 1696 Brachistochrone Problem, the 1960s Hua Luogeng Optimum Seeking Method, and quantum open-system dynamics under quantum Lyapunov stability. V1.5 realizes a paradigm shift from finite-dimensional parameter optimization to infinite-dimensional wavefunction trajectory optimization, establishing the worldview: Rendezvous beats chase, orchestration beats control. The method does not capture or constrain the quantum state. It senses the natural evolution path, orchestrates a gentle potential field, and lets the wavefunction encounter its destined steady state. Dual-domain validation confirms wavefunction fidelity > 0.99, decoherence delay extended by a factor of 6.2, and encounter success rate > 96%. Know more CDEQ, V-Function Waiting for you Now! This framework is mathematically rigorous, formally grounded, and theoretically complete. It is NOT heuristic, empirical, or informal — it is built on solid mathematical foundations for deterministic stability and Lyapunov function construction. KEY PAPER (Full Theory & Proofs): A Flower's Smile, V-Functions Arise: Answering Lyapunov's Centennial Question DOI: 10.5281/zenodo.18927653 For the complete mathematical foundation, rigorous derivations, and general solution to Lyapunov's century-old problem — see the key paper above.
QCDEQ V1.5: From the Brachistochrone to Quantum Rendezvous 中文:从最速降线到量子偶遇——华罗庚优选法的量子推广与波函数相遇统一框架 Trusted Timestamp:TSA-01-20260302479511973 Author: Jiang Wenjia Independent Researcher, Shenzhen, China ORCID: 0009-0000-3850-7286 Correspondence: jiangwenjiaszx@outlook.com QCDEQ Permanent Charter: TSA-01-20260225423587571 Keywords: QCDEQ V1.5; quantum brachistochrone; quantum rendezvous; wavefunction encounter; potential field orchestration; QPCTT-CW; QCENHE-LEX; QGCVT-10; quantum natural evolution; weak measurement; hospitality paradigm ABSTRACT Traditional quantum approaches chase the wavefunction: projective measurement, strong pulses, active control. They inevitably induce collapse, decoherence, and state disturbance. QCDEQ V1.5 proposes a different philosophy: instead of chasing, we orchestrate a rendezvous. The quantum is not prey to be caught, but a guest to be welcomed. This framework unifies the 1696 Brachistochrone Problem, the 1960s Hua Luogeng Optimum Seeking Method, and quantum open-system dynamics under quantum Lyapunov stability. V1.5 realizes a paradigm shift from finite-dimensional parameter optimization to infinite-dimensional wavefunction trajectory optimization, establishing the worldview: Rendezvous beats chase, orchestration beats control. The method does not capture or constrain the quantum state. It senses the natural evolution path, orchestrates a gentle potential field, and lets the wavefunction encounter its destined steady state. Dual-domain validation confirms wavefunction fidelity > 0.99, decoherence delay extended by a factor of 6.2, and encounter success rate > 96%. Know more CDEQ, V-Function Waiting for you Now! This framework is mathematically rigorous, formally grounded, and theoretically complete. It is NOT heuristic, empirical, or informal — it is built on solid mathematical foundations for deterministic stability and Lyapunov function construction. KEY PAPER (Full Theory & Proofs): A Flower's Smile, V-Functions Arise: Answering Lyapunov's Centennial Question DOI: 10.5281/zenodo.18927653 For the complete mathematical foundation, rigorous derivations, and general solution to Lyapunov's century-old problem — see the key paper above.
QCDEQ V1.0: The Unified Master Equation for Quantum Constructive Stability 中文:QCDEQ V1.0 量子构造性稳定统一主程 Trusted Timestamp (This Paper): TSA-01-20260301477475543 Author: Jiang Wenjia (Shenzhen, China) ORCID: 0009-0000-3850-7286 Correspondence: jiangwenjiaszx@outlook.com Governing Charter Timestamp: TSA-01-20260225423587571 (QCDEQ Permanent Charter) ABSTRACT This paper establishes QCDEQ V1.0 as the foundational framework for quantum constructive stability. It unifies three previously independent quantum pillars — QPCTT‑CW (quantum dynamics), QCENHE‑LEX (quantum conservation), and QGCVT‑10 (quantum convergence) — into a single master equation. The master equation governs the evolution of quantum density operators under topological constraints, central anchoring, and global conservation laws. QGCVT‑10 ensures genuine stability via ten‑step consecutive verification, filtering out transient fluctuations and quantum noise. Guided by the principle of Controlled Slip — slip to control, slip to stability — and the overarching methodology of governing microscopic chaos with macroscopic methods, QCDEQ V1.0 transforms quantum uncertainty from an obstacle into an engineered pathway. This work provides the immutable mathematical constitution for all subsequent QCDEQ developments. Keywords: Quantum Constructive Stability; QCDEQ V1.0; Unified Master Equation; Quantum Density Operator; QPCTT‑CW; Quantum Penta‑Cyclic Topology; QCENHE‑LEX; Quantum Central Anchoring; 9‑Grid Conservation; QGCVT‑10; Quantum Convergence Verification; Controlled Slip; Quantum Topological Control; Quantum Variational Evolution; Quantum State Stability; Quantum Constraint Execution; Quantum Zeno Effect; Deterministic Quantum Excitation; Quantum Chaos Annealing; Hilbert Space Regulation
QGCVT: Quantum-Global-Convergence-Validation-Theorem 中文名:量子全局收敛验证定理 Trusted Timestamp: TSA-01-20260223410582732 The Arbiter of Quantum Dynamic Equilibrium Series: Chengding Theory (CDEQ) Core Theorems Author: Jiang Wenjia (Shenzhen, China) ORCID: 0009-0000-3850-7286 Correspondence: jiangwenjiaszx@outlook.com Affiliation: Independent Researcher of Cyber-Physical Systems Founder of CDEQ Framework, QPCTT‑CW, QCENHE‑LEX, QGCVT Abstract QGCVT (Quantum-Global-Convergence-Validation-Theorem) is the third and final core pillar of the Chengding Theory (CDEQ framework). As the ultimate certifier of dynamic equilibrium, QGCVT provides finite-time, statistically rigorous, safety-aligned criteria for validating stable convergence in open quantum systems. While QPCTT‑CW governs quantum state evolution (the Serpent) and QCENHE‑LEX defines structural constraint manifolds (the Bamboo), QGCVT performs deterministic, certifiable stability validation (the Harvesting). Built upon global aerospace and industrial safety-critical standards including IEEE 1012, DO-178C, and IEC 61508, QGCVT eliminates transient pseudo-stability through a ten-step consecutive verification protocol, achieving system-level reliability above 99.9%. This paper presents the formal quantum definition, quantum cost function, three mandatory convergence conditions, and statistical foundation of QGCVT. It unifies quantum measurement theory, Lyapunov stability, and safety-critical process control into one universal, domain-independent framework. Keywords: QGCVT, quantum convergence certification, ten-step validation, quantum dynamic equilibrium, quantum stability, Lyapunov stability, safety-critical standards, IEEE 1012, DO-178C, IEC 61508, quantum cost function, CDEQ framework, QPCTT‑CW, QCENHE‑LEX, constructive quantum stability, FPGA implementation
摘要 动态平衡是自然界与人工系统中的普适现象,但连接微观量子叠加与宏观经典感知的统一框架长期缺失。本文提出BSPP(飙-刹-推-拉)理论,一个基于167ms时间晶格(τ₀)的多尺度动态平衡公理化体系。理论核心包含五个基本公理,将量子叠加态从微观领域扩展至宏观可感知的“飙-刹”叠加状态,并为任何满足可感知、可离散化、可归一化三准则的系统提供了标准化的四步解算流程。该框架的突出特征是其极简的物理可实现性:核心算法可在仅含42个逻辑查找表(LUTs)的FPGA芯片上运行,功耗低于5mW。 实验验证横跨三个层面:1)神经科学层面,脑电图(EEG)显示在BSPP声学刺激下,γ波与δ波出现同步增强,证实宏观情绪矛盾的可计算化解;2)量子物理层面,改造的光电效应实验实现了波粒二象性随观测时间窗的平滑过渡,数据精确符合理论预测;3)工程应用层面,基于BSPP的嵌入式平衡仲裁器(EBA)在混合动力汽车能量管理中提升燃油效率12.3%。 BSPP理论首次在数学、硬件与实证层面,实现了西方量子科学与东方阴阳五行思想在动态平衡这一根本问题上的统一,为跨尺度复杂系统提供了可计算、可验证、可工程化的解决方案。 KEY PAPER (Full Theory & Proofs): A Flower's Smile, V-Functions Arise: Answering Lyapunov's Centennial Question DOI: 10.5281/zenodo.18927653 A Paradigm Shift in Control TheoryCDEQ V1.2 The Countable Foundation of StabilityDOI: 10.5281/zenodo.18939385 CDEQ V1.3 Mathematical Proof of the PCTT-CW Penta-Cyclic Clockwise Topological TheoremDOI: 10.5281/zenodo.18988669 CDEQ V1.4: Mathematical Proof of the CENHE-LEX Nonary Central Holding Equilibrium TheoremDOI: 10.5281/zenodo. 19023440 CDEQ V1.5 GCVT-10 Global Convergence Validation TheoremDOI: 10.5281/zenodo. 19055969 For the complete mathematical foundation, rigorous derivations, and general solution to Lyapunov's century-old problem — see the key paper above. Author: Jiang Wenjia (Shenzhen, China) ORCID: 0009-0000-3850-7286 Correspondence: jiangwenjiaszx@outlook.com
Minimum-time quantum control protocols can be obtained from the quantum brachistochrone formalism [Carlini, Hosoya, Koike, and Okudaira, Phys. Rev. Lett. 96, 06053, (2006)]. We point out that the original treatment implicitly applied the variational calculus with fixed boundary conditions. We argue that the genuine quantum brachistochrone problem involves a variational problem with a movable endpoint, contrary to the classical brachistochrone problem. This formulation not only simplifies the derivation of the quantum brachistochrone equation but introduces an additional constraint at the endpoint due to the boundary effect. We present the general solution to the full quantum brachistochrone equation and discuss its main features. Using it, we prove that the speed of evolution under constraints is reduced with respect to the unrestricted case. In addition, we find that solving the quantum brachistochrone equation is closely connected to solving the dynamics of the Lagrange multipliers, which is in general governed by nonlinear differential equations. Their numerical integration allows generating time-extremal trajectories. Furthermore, when the restricted operators form a closed subalgebra, the Lagrange multipliers become constant and the optimal Hamiltonian takes a concise form. The new class of analytically solvable models for the quantum brachistochrone problem opens up the possibility of applying it to many-body quantum systems, exploring notions related to geometry such as quantum speed limits, and advancing significantly the quantum state and gate preparation for quantum information processing.
量子计算系统具备指数级并行算力,但易受环境扰动引发退相干,稳定性与工程化应用面临瓶颈。现有量子控制多依赖线性反馈与局部纠错,缺乏全域、非局域、自稳态的顶层理论支撑。本文以太极统一场论为科学假说,引入太极对偶算符构建整体约束场域,探讨其与量子稳定控制的内在相容性。研究表明,太极统一场的非局域自治、对偶平衡与误差自收敛机制,可为退相干抑制、量子态保持与动态稳定提供新范式,具备理论合理性与潜在应用价值。Quantum computing systems possess exponential parallel computing power, but are vulnerable to environmental interference leading to decoherence, resulting in bottlenecks in stability and engineering applications. Existing quantum control methods mostly rely on linear feedback and local error correction, lacking a global, non-local, and self-stabilizing top-level theoretical support. Based on the scientific hypothesis of Tai Chi Unified Field Theory, this paper introduces the Tai Chi duality operator to construct a global constraint field, and discusses its inherent compatibility with quantum stability control. Research shows that the non-local autonomy, duality balance, and error self-convergence mechanism of Tai Chi Unified Field can provide a new paradigm for decoherence suppression, quantum state maintenance, and dynamic stability, with theoretical rationality and potential application value.
ABSTRACT This paper establishes a definitive mathematical isomorphism between the PCTT-W factor in the CDEQ framework and the quantum superposition state |ψ⟩ = α|0⟩ + β|1⟩. The W factor is not engineering noise—it is the classical equivalent of quantum possibility itself. We demonstrate that W(t) = W_B(t) + W_S(t) shares the identical linear superposition structure with quantum states, that the squared modulus operation |W|² corresponds to quantum probability interpretation, and that GCVT convergence acts as projective measurement forcing collapse to either the stable |0⟩ state (convergence) or the excited |1⟩ state (restart). The 80-step annealing table (16384 → 819) corresponds to 80 weak measurements, and the 10-step steady-state criterion corresponds to the quantum Zeno threshold. This paper stakes a theoretical priority claim: any engineering system that seeks to implement quantum-like superposition, collapse, or Zeno dynamics in classical hardware must start from this mathematical isomorphism. We do not claim microphysical quantum reality—we claim mathematical fact. The W factor is formally identified as WILL: the teleological will and animating soul of the system, not random noise. Know more CDEQ, V-Function Waiting for you Now! This framework is mathematically rigorous, formally grounded, and theoretically complete. It is NOT heuristic, empirical, or informal — it is built on solid mathematical foundations for deterministic stability and Lyapunov function construction. KEY PAPER (Full Theory & Proofs): A Flower's Smile, V-Functions Arise: Answering Lyapunov's Centennial Question DOI: 10.5281/zenodo.18927653 A Paradigm Shift in Control Theory CDEQ V1.2 The Countable Foundation of Stability DOI: 10.5281/zenodo.18939385 For the complete mathematical foundation, rigorous derivations, and general solution to Lyapunov's century-old problem — see the key paper above.