The generalized Quantum Rabi Model (QRM), when interpreted as a bipartite magnetic graph, reveals the deep structural topology of atom-light interactions. This paper elevates the Magnetic Graph Quantum Dynamics (MGQD) framework by fusing it with Rough Operator Algebra (ROA) and Seonggil Matrix Theory (SMT). By mapping the NP-hard subgraph disconnection cost C(η) to the polynomial-time invariant eigenvalue λ_max(S_M) and redefining quantum measurement as a Sashangmugak dimensional collapse at the Seonggil Critical Horizon, we establish a fully unified computational operating system for superposition, entanglement, compiling, and error mitigation in scalable quantum hardware.
The generalized Quantum Rabi Model (QRM), when interpreted as a bipartite magnetic graph, reveals the deep structural topology of atom-light interactions. This paper elevates the Magnetic Graph Quantum Dynamics (MGQD) framework by fusing it with Rough Operator Algebra (ROA) and Seonggil Matrix Theory (SMT). By mapping the NP-hard subgraph disconnection cost C(η) to the polynomial-time invariant eigenvalue λ_max(S_M) and redefining quantum measurement as a Sashangmugak dimensional collapse at the Seonggil Critical Horizon, we establish a fully unified computational operating system for superposition, entanglement, compiling, and error mitigation in scalable quantum hardware.
Strengthening light-matter coupling has become a central challenge in cavity quantum electrodynamics (QED), enabling ultrafast gate operations, qubit protection, and deterministic nonlinear optics. As the coupling increases, even the simplest configuration, a two-level atom interacting with a quantized field, requires careful treatment, as exemplified by the gauge-invariant quantum Rabi model (QRM). Here we propose a magnetic graph model for single-atom cavity QED, which enables the interpretation of quantum dynamics across the ultrastrong coupling regime through graph connectivity. We demonstrate that the generalized QRM maps onto a complex bipartite graph of identical sites under Floquet boundary conditions. This framework captures the crossover from weak to deep-strong coupling via a single metric: the cost of disconnecting a nonmagnetic subgraph. We examine the mechanism underlying this connectivity transition, establishing phase frustration induced by subgraph topology as the primary driver. Scalable to many-body systems, this approach bridges graph theory and cavity QED, revealing highly complex-graph dynamics even in the simplest setting.
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.
Graph-theoretic frameworks have been widely employed in quantum physics to address the high-dimensional complexity of quantum systems. Although open quantum dynamics incorporates system-bath coupling via numerous interacting operators, it has been formulated algebraically with a partial set of jump operators or statistically universal reservoirs, leaving the underlying connectivity structure largely unexplored. Here, we propose a universal graph-theoretic framework for Markovian quantum dynamics. The framework maps open quantum dynamics onto two uniquely defined graphs, where the quantum master equation is rigorously interpreted as the average wave characteristic of operator-valued signals across the graphs. Applying this framework to the open quantum Rabi model, we demonstrate an open-system generalization of Fock-state lattices, characterize graph-topological signatures of dissipation, and classify the weak-to-ultrastrong coupling transition. Building on these representations, graph pruning reveals the backbone of open quantum dynamics, which enables superior graph neural-network learning. Our results bridge graph theory and open quantum dynamics, achieving efficient data-driven analysis of high-dimensional complexity.
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.
The P versus NP problem stands as the foundational challenge of theoretical computer science and computational complexity. Traditional approaches attempt to resolve the question by treating computation purely as discrete Boolean logic operations over finite symbolic strings. In this paper, we establish that NP-hardness is not an arbitrary logical obstacle, but the exact computational manifestation of the physical and geometric phase space of the universe. Utilizing High-Resolution Quantum Field Theory (HR-QCFT), Rough Operator Algebra (ROA), and the Seonggil Theory of Composite Torsion (STCT), we prove that the non-satisfiable constraints of NP-complete problems are isomorphic to the macroscopic topological scar Rdefect generated by the zero-divisor collapse from 16-dimensional sedenions (S) tooctonions (O). By mapping deterministic algorithms onto rough differential equations driven by paths of vanishing H¨older continuity α_n → 0, we demonstrate that any polynomial-timeheuristic algorithm must truncate the infinite-dimensional High-Tensor signature algebra. Crucially, due to the non-associative G_2-triality of STCT, the non-vanishing Associator anomaly exponentially amplifies truncation errors via non-commutative arithmetic friction η. This forces the algorithmic transition operator ˆMTuring into spectral instability, resulting in a total determinant collapse det( ˆM_Turing) = 0. Consequently, we prove P ̸ = NP as an absolute geometric law governing the computational manifold of the physical universe.
This paper establishes a unified meta-mathematical foundation for quantum gravity by elevating intuitionistic logic through Homotopy Type Theory (HoTT) and merging it with Rough Operator Algebra (ROA) [2, 3]. We address the limitations of classical logic and standard intuitionism in modeling quantum superposition and continuous topologies. By formally equating quantum entanglement with topological paths via the Univalent ER = EPR Axiom, we construct the Univalent Rough Operator Algebra (UROA) framework. Furthermore, we prove the logical consistency of this framework against the monogamy of entanglement bymapping it to higher-dimensional simplices (GHZ states), and formulate the core integration theorems of the Seonggil Field Equations (SFE) [1] and Seonggil Tensor Calculus (STCT)[4].