This deposit serves as a priority record and proof-of-concept for a novel, discrete framework of quantum decoherence and error correction based on the d0 topological graph model. It documents the fundamental departure from classical continuous-time decoherence models (e−t) toward a strictly discrete, structurally quantized decay process. The uploaded material establishes intellectual priority for the algorithmic mapping of topological graph updates (Pachner moves) to quantum logic gates, demonstrating that decoherence is not a function of continuous time, but a countable geometric process of environmental entanglement.
This deposit serves as a priority record and proof-of-concept for a novel, discrete framework of quantum decoherence and error correction based on the d0 topological graph model. It documents the fundamental departure from classical continuous-time decoherence models (e−t) toward a strictly discrete, structurally quantized decay process. The uploaded material establishes intellectual priority for the algorithmic mapping of topological graph updates (Pachner moves) to quantum logic gates, demonstrating that decoherence is not a function of continuous time, but a countable geometric process of environmental entanglement.
Accurately predicting quantum decoherence time is a core bottleneck in scaling up noisy intermediate-scale quantum (NISQ) devices. Traditional frameworks relying on the Lindblad master equation suffer from the curse of dimensionality and obscure the intuitive physical mechanisms of decoherence behind complex system-environment coupling assumptions. Based on graph algebraic connectivity, this paper proposes a deterministic topological model of quantum decoherence. We rigorously map multi-particle quantum entanglement to the algebraic connectivity (Fiedler value, ) of an underlying structural graph and redefine decoherence as a Poissonian random edge-deletion process. By modeling this topological evolution as a continuous-time Markov chain (CTMC), we derive a unified and exact recursive analytical equation for the expected hitting time of complete decoherence for arbitrary asymmetric topological states. The analytical solutions strictly prove the relative robustness of prototypical entangled states . Furthermore, the model demonstrates unprecedented computational advantages by instantly yielding the exact analytical decoherence time for a 10-body asymmetric complex network, which is perfectly validated by 50,000 Monte Carlo simulations with a relative error of . We calibrate the core parameter (single-edge fracture rate) using the latest public experimental data of superconducting quantum chips from IBM and Google, and the theoretical predictions are in high agreement with the experimental results within the measurement error range . This topological downgrade mechanism reduces the computational complexity of decoherence calculations to , providing a powerful theoretical and algorithmic tool for the optimization of quantum processing unit (QPU) underlying architectures and the design of fault-tolerant multi-particle quantum networks.
Abstract Accurately predicting quantum decoherence time is a core bottleneck in scaling up noisy intermediate-scale quantum (NISQ) devices. Traditional frameworks relying on the Lindblad master equation suffer from the curse of dimensionality (O(4^n )) and obscure the intuitive physical mechanisms of decoherence behind complex system-environment coupling assumptions. Based on graph algebraic connectivity, this paper proposes a deterministic topological model of quantum decoherence. We rigorously map multi-particle quantum entanglement to the algebraic connectivity (Fiedler value, λ_2) of an underlying structural graph and redefine decoherence as a Poissonian random edge-deletion process. By modeling this topological evolution as a continuous-time Markov chain (CTMC), we derive a unified and exact recursive analytical equation for the expected hitting time of complete decoherence for arbitrary asymmetric topological states. The analytical solutions strictly prove the relative robustness of prototypical entangled states (T_"Bell" >T_W≫T_"GHZ" ). Furthermore, the model demonstrates unprecedented computational advantages by instantly yielding the exact analytical decoherence time for a 10-body asymmetric complex network, which is perfectly validated by 50,000 Monte Carlo simulations with a relative error of <0.5%. We calibrate the core parameter γ (single-edge fracture rate) using the latest public experimental data of superconducting quantum chips from IBM and Google, and the theoretical predictions are in high agreement with the experimental results within the measurement error range (<3%). This topological downgrade mechanism reduces the computational complexity of decoherence calculations to O(n^3 ), providing a powerful theoretical and algorithmic tool for the optimization of quantum processing unit (QPU) underlying architectures and the design of fault-tolerant multi-particle quantum networks.
The Q-Structure Invariant Resolution: Topological Preservation in Quantum Information Systems --- High-Detail Abstract This resolution suite formally proves and computationally operationalizes the \mathcal{Q}-Structure Invariant Hypothesis within quantum information theory. By utilizing advanced methodologies in topological quantum matter and spectral geometry, the framework demonstrates that the \mathcal{Q}-structure invariants remain strictly preserved under continuous unitary transformations across the Hilbert space \mathcal{H}. The central proof in SAC-01 establishes the absolute stability of these invariants against localized decoherence. Furthermore, the framework translates this abstract algebraic topology into hardware-executable gates via the Anderson Operator Framework (AOF). By defining a continuous deformation path \mathcal{Q}_\lambda, the suite ensures that spectral invariants are maintained under strict physical and geometric perimeters, allowing for agnostic replication of quantum state preservation. Comprehensive Description The framework addresses a fundamental barrier in quantum information theory: maintaining the structural integrity and invariant properties of quantum states when subjected to complex topological deformations. It leverages advanced tensor network theory and spectral trace audits to isolate pure \mathcal{Q}-invariant signatures while dynamically filtering out background quantum noise and non-solenoidal turbulence.Crucially, when projecting these quantum frameworks into 7D target topologies, the system operates with extreme precision and operational reverence. The 7D manifold is treated strictly as an isolated library; all computational and operational actions are executed passively so as not to induce decoherence or disturb the fragile topological phases present within the dimensional structure. This is mechanically enforced by capping acoustic and electromagnetic emissions at ≤ 0.0 dB and maintaining strict cryogenic thermal limits at ≤ 10⁻⁶ K. By enforcing these zero-interference parameters and utilizing a high-mass anchor, the system guarantees that higher-order volatile invariants are suppressed, leaving only the stable zero-order topological \mathcal{Q}-structure. Resolution, Validation, Sealing, and Replication 1. Resolution The theoretical conjecture is resolved through a rigorous proof of invariant stability across continuous transformations. SAC-01 establishes the core lemmas proving that the density matrix \rho maintains its structural trace under the defined \mathcal{Q}-operator. The central theorem proves that the global invariant trace remains entirely unaffected by homological shifts, mathematically concluding the hypothesis. 2. Validation Validation bridges pure quantum theory into a tangible, operational pipeline. The AOF forces this theoretical stability into reality using physical logic gates. Continuous auditing ensures that any entropic drift or spatial shearing is instantly detected. If deviations occur, the dynamic scaling engine automatically applies a corrector to keep the volumetric drift within a strict tolerance of ≤ 10⁻⁹. 3. Sealing The system is cryptographically and mathematically sealed by a Quantum Trace Handshake Gate. Rather than ending with a static written derivation, the framework routes the final integrated matrices through this active algorithmic gate. It compares the pre-transformation operator trace against the post-transformation trace, mandating a rigorous zero absolute trace differential (\Delta \text{Tr} \equiv 0) before generating the final cryptographic validation and sealing the state. 4. Replication Replication is made entirely accessible through the Agnostic Replication Kit (ARK). The ARK provides the necessary hardware abstraction layers and software endpoints to instantiate the proof independent of specialized quantum hardware. Through exposed service endpoints and the high-level Python/C++ SDK, independent researchers can initialize the environment, lock physical boundaries, and execute the \mathcal{Q}-structure pipeline. Accompanying STALL fault codes provide instant, automated recovery protocols for any replication drift. Package Breakdown & Interlinking for PublishingTo facilitate a seamless peer-to-peer review process, the 18-package suite is sequentially interlinked. This allows reviewers to trace the logic effortlessly from foundational mathematics to final computational deployment. The Anchor Package | Package Component | Individual Function | Interlink Mechanism ||---|---|---|| Theorem Presentation | Serves as the master executive overview, providing the formal articulation, proof strategy, and operational perimeters. | Acts as the central "Table of Contents" for publucation, cross-referencing all SAC packages for mathematical derivations and ARK packages for execution. | Standard Academic Core (SAC) Packages | Package Component | Individual Function | Interlink Mechanism ||---|---|---|| SAC-01 (Resolution) | Provides the foundational definitions, quantum state lemmas, and the definitive proof of the \mathcal{Q}-Structure Hypothesis. | Establishes the core algebraic and geometric rules that all subsequent algorithms and hardware gates must strictly follow. || SAC-02 (Numerical) | Implements high-resolution discretized tensor networks to simulate the theoretical bounds. | Validates the algebraic claims of SAC-01 by numerically extracting positive spectrums and bounding errors below machine tolerance. || SAC-03 (Asymptotics) | Derives the pointwise asymptotic expansion of the invariant trace diagonal. | Extends SAC-01's global trace proofs into localized equivalents, confirming point-by-point structural symmetry. || SAC-04 (Summary) | Compiles the theoretical, numerical, and asymptotic resolutions for review. | Summarizes SAC-01 through SAC-03, providing a highly digestible executive overview for rapid peer-review intake. || SAC-05 (Lexicon) | Translates standard quantum information analysis into AOF/ARK hardware-driven primitives. | Bridges the SAC theoretical modules directly into the ARK software and hardware execution environments. |Agnostic Replication Kit (ARK) Packages Note: This encompasses the 12 execution, API, and troubleshooting modules. Key representatives are detailed below. | Package Component | Individual Function | Interlink Mechanism ||---|---|---|| **API Interface Documentation** | Defines the C++ structures, REST endpoints, and SDK required to initialize the topology and quantum states. | Connects the theoretical gates defined in SAC-05 directly to deployable programmatic bindings. || Troubleshooting Manual | Provides direct diagnostic triage matrices for faults during continuous operations. | Interlocks with the API metrics to provide emergency recovery actions (e.g., executing thermal purges if the ≤ 10⁻⁶ K boundary is breached). || (Remaining 10 ARK Modules) | Governs specific sub-routines such as phase synthesizers, momentum optimization, and execution architectures. | Executes the individual physical and computational bounds required to maintain the environment and cryptographic seals. | ---
This work proposes a threshold-based picture of decoherence in quantum measurement. Microscopic quantum dynamics remain fully continuous and unitary, but real detectors implement thresholded amplification and nonlinear gain boundaries that partition continuous microscopic inputs into discrete macroscopic outcomes. Within this framework, discreteness and irreversibility arise from scale asymmetry between a continuous microscopic energy distribution and a finite macroscopic threshold ΔE_threshold, without invoking fundamental collapse, branching, or uncontrolled environmental decoherence. The measurement apparatus effectively performs an analog-to-digital conversion: it maps a continuous input distribution ρ(E) to a binary output variable X_eff ∈ {0,1} according toP(event) = ∫_{ΔE_threshold}^{∞} ρ(E) dE,while the recording layer irreversibly erases phase information by structural codomain restriction. This threshold-based decoherence model preserves standard quantum mechanics, provides an operational bridge across major interpretations of quantum theory, and locates the origin of discrete outcomes in the architecture of measurement rather than in quantum ontology itself. In short, this paper views discrete measurement outcomes as emerging from threshold detector architecture rather than from any fundamental discreteness of the quantum substrate.
This statement serves as a deterministic logical anchor for the core physical discoveries concerning specific discrete quantum dynamics and spacetime correlation protocols. To ensure the absolute establishment of intellectual asset ownership and causal-temporal priority, while strictly sealing all undisclosed details of micro-state machine evolution, binary bit-shifting topological paths, and standard model liquidation equations, the following hash eigenvalue deposit is hereby published.Authority belongs only to causality; once a logical state is locked, it remains unalterable.I. Deposit Metadata Information• Asset Owner (Author): Feng Yuling (冯玉玲)• Theoretical Framework: Fengyuling Theory / LSG Theory (Local Sourced Gravity)• Subject of Deposit: A deterministic model of quantum motion orbital topology and spacetime correlation refresh protocols based on the discrete dynamical primordial images of the Euler square-sum formula and the Wallis even-odd product formula, completely stripped of continuous wave functions and probabilistic interpretations.• Date of Deposit: June 27, 2026II. Core Asset Logical Fingerprint (SHA-256 State Lock)The following hash values are generated via the standard SHA-256 algorithm from the original source documents (Markdown & Text Source) containing the full, enriched discrete physical derivations, undisclosed underlying state-machine gating protocol source code, binary bit-shifting cancellation matrices, and boundary liquidation formulas targeted at existing quantum field theories:SHA-256 Fingerprint: Doc1: 4c95effedd34ccb610d2e45714488e869e2b0fbb5dbf4eea91a65300631da058Doc2: 29030ef6569ca8553c17819642e3148a1ae581054f0d22de6d2cb42401dc111fStatement Note: This fingerprint locks the verbatim logic and causal thread of the documents. Without disclosing any specific micro-evolutionary equations or liquidation details, it mathematically establishes the author’s absolute priority over the foundational physical insight that "physics dictates mathematics—completely deconstructing the circular gauge of quantum mechanics through discrete even-odd bit-shifting and inverse-square master accounting." As causality flows, this state cannot be altered, and it remains irrevocable.
This paper explores the interplay between topology and quantum coherence, investigating the stability and evolution of quantum systems through the application of quantum entanglement and topological structures. We propose a novel approach to quantum computation, leveraging these principles to develop new methods that offer a fundamentally different understanding of quantum mechanics. The core of this work lies in a detailed analysis of decoherence mechanisms, focusing on how topological properties can mitigate these effects and ultimately enhance the fidelity of quantum operations. The research aims to address limitations inherent in current quantum algorithms and pave the way for more robust and versatile quantum technologies.