Formalism of Quantum Layer Energy Dynamics (QLED): A Non-Linear Topological Framework for a Deterministic Universe

Murat Durna, Artificial Intelligence (Analysis Assistance)

Murat Durna, Artificial Intelligence (Analysis Assistance)

Rogerio Junior, Estevan Rychard

Quantum Key Distribution (QKD) provides unconditional security guaranteed by the laws of quantum mechanics. However, practical implementations remain vulnerable to physical-layer intrusions, such as the Photon-Number-Splitting (PNS) attack, which exploits non-ideal multi-photon emissions. Current countermeasures heavily rely on asymptotic statistical error bounds or complex optical hardware, introducing inherent detection latency. Building upon our foundational theoretical framework of fractal-entropic scaling, we introduce a protocol-agnostic, deterministic detection framework grounded in the dynamics of open quantum systems. We establish an operational isomorphism between the purity loss (ΔSL) induced by an eavesdropper and the topological symmetry breaking of nonlinear dynamic systems in the complex plane. By mapping discretized stochastic noise into a generalized complex iterative map, microscopic quantum perturbations are non-linearly amplified, forcing an orbital divergence in finite time. Hardware validation via fixed-point arithmetic on a Field-Programmable Gate Array (FPGA) demonstrates real-time, Layer-1 intrusion detection without relying on ideal quantum measurements. Using the BB84 protocol as a canonical case study, we prove that active quantum eavesdropping is topologically incompatible with the continuous natural noise of a secure channel.

Kim Joris Boström

Yassin Tanan

Recent breakthroughs in many-body quantum dynamics have unexpectedly revealed that the growth of entanglement entropy and quantum decoherence strictly follow the Kardar-Parisi-Zhang (KPZ) universality class, an equation originally formulated to describe macroscopic stochastic surface growth. In this paper, we theoretically bridge this empirical observation with the Dynamic Metric Topology (DMT) framework. We demonstrate that the macroscopic "roughness" governed by the KPZ equation in quantum spin systems is not driven by fundamentally stochastic noise, but by a deterministic topological friction between the spinorial phase and the scalar field pseudo-Riemannian manifold. By explicitly mapping the KPZ non-linear growth term to the DMT scalar impedance threshold at H˜ = 114.12 GeV via the fine structure constant (α), we provide a unified tensorial master equation. This integration redefines quantum noise as an uncompensated metric drag, providing a definitive proof through the deterministic evolution of Bell’s inequality parameters.

Giovanni de Felice, Boldizsár Poór, Cole Comfort +4 more

Photonic systems offer a promising platform for interconnecting quantum processors and enabling scalable, networked architectures. Designing and verifying such architectures requires a unified formalism that integrates linear algebraic reasoning with probabilistic and control-flow structures. In this work, we introduce a graphical framework for distributed quantum computing that brings together linear optics, the ZX-calculus, and dataflow programming. Our language supports the formal analysis and optimization of distributed protocols involving both qubits and photonic modes, with explicit interfaces for classical control and feedforward, all expressed within a synchronous dataflow model with discrete-time dynamics. Within this setting, we classify entangling photonic fusion measurements, show how their induced Pauli errors can be corrected via a novel flow structure for fusion networks, and establish correctness proofs for new repeat-until-success protocols enabling arbitrary fusions. Layer by layer, we construct qubit architectures incorporating practical optical components such as beam splitters, switches, and photon sources, with graphical proofs that they are deterministic and support universal quantum computation. Together, these results establish a foundation for verifiable compilation and automated optimization in networked quantum computing.