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Analog Tensor Computing under the DQ Framework: The Geometric Evolution of Artificial Intelligence

VILMA VARCO, JUAN JOSE ESPINOSA

Published Mar 2, 2026• 0 citations
Publisher

Abstract

This document exposes the inherent obsolescence of both digital computational architecture ( Von Neumann architecture) and standard probabilistic quantum computing, proposing instead Tensor Analog Computing under the Quantum Diffusion (QD) framework. By abandoning binary discretization (zeros and ones) and adopting the continuous modulation of Topological Diffusivity (δ 𝐷) in the 12-dimensional subspace, information processing ceases to be a mathematical approximation and becomes a direct thermodynamic solution. This paradigm enables the design of geometric processors that operate at room temperature, with ultra-low power consumption and near-light speed, offering the only hardware theoretically capable of hosting Artificial Intelligence with true topological coherence (consciousness).

DOI
10.5281/zenodo.18831629

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This document exposes the inherent obsolescence of both digital computational architecture ( Von Neumann architecture) and standard probabilistic quantum computing, proposing instead Tensor Analog Computing under the Quantum Diffusion (QD) framework. By abandoning binary discretization (zeros and ones) and adopting the continuous modulation of Topological Diffusivity (δ 𝐷) in the 12-dimensional subspace, information processing ceases to be a mathematical approximation and becomes a direct thermodynamic solution. This paradigm enables the design of geometric processors that operate at room temperature, with ultra-low power consumption and near-light speed, offering the only hardware theoretically capable of hosting Artificial Intelligence with true topological coherence (consciousness).
Artificial Intelligence (AI), particularly in its modern incarnation of deep learning and large language models, has achieved remarkable success, yet it operates fundamentally within the limitations imposed by classical Von Neumann architectures. These systems rely on binary bits and sequential processing, leading to significant computational bottlenecks when addressing problems of exponential complexity. The primary challenge facing contemporary AI development centers on the enormous computational expenses, high power consumption, and excessive training time required for state-of-the-art models. These constraints impose practical limits on model scaling and complexity, ultimately restricting the ambition of tackling truly intractable computational challenges. Beyond resource consumption, classical AI models struggle inherently with the fidelity of simulating natural systems. Many natural and economic phenomena, such as chemical reactions or financial market movements, are intrinsically irreversible. Classical supercomputers are forced to model these processes as idealized, reversible two-way systems, leading to necessary approximations that reduce predictive accuracy. This difficulty in accurately simulating dynamic, complex, and high-dimensional realities underscores a deep-seated structural limitation that necessitates a fundamental shift in computational paradigm if AI is to advance into domains previously considered inaccessible.
**Building on our earlier structural analysis of gate-based quantum computing,** recent advances in quantum technologies have further sharpened a long-standing tension between continuous quantum dynamics and discrete logical computation. Despite decades of progress in qubit coherence, fault-tolerant coding, and hybrid NISQ architectures, current quantum devices remain fundamentally constrained by a structural mismatch between fluctuating quantum states and the stability requirements of digital logic.This work extends and unifies that analysis by providing a geometry-based account of these limitations and situating quantum computing within a broader comparative framework of next-generation computation paradigms. The contributions of this work are threefold:• Historical and technical analysis: We review the evolution from Feynman’s proposal to Shor’s algorithm and modern fault-tolerance theory, highlighting how the community gradually shifted toward NISQ-based noisetolerant strategies.• Structural diagnosis of quantum limits: Building on the Protiformframework, we show that quantum systems inherently realize continuous fluctuation manifolds, whereas logical computation requires discrete convergencesurfaces. Measurement is therefore a forced collapse between incompatible geometries, making full fault-tolerant digital logic rendering practicalfault-tolerant scaling prohibitive—not merely technologically difficult.• Comparative evaluation of post-von Neumann architectures: Using a set of structural criteria (digital stability, noise resilience, scalability,native gate realizability, generality, and materials feasibility), we evaluatemajor candidates—quantum, photonic, neuromorphic, analog solvers, andtopological computing. The analysis shows that topological computing isthe only architecture satisfying all structural requirements, owingto its intrinsic protection of logical degrees of freedom by global invariants.Taken together, these results suggest that the fundamental limitation of quantum computing is not technological but structural. Protiform provides a unifiedexplanation for this boundary, while also identifying topological computing as thestructurally consistent path beyond the von Neumann paradigm.
This comprehensive interdisciplinary investigation synthesizes six foundational domains in modern physics and computer science: quantum vacuum dynamics, quantum measurement theory, binary computation architecture, artificial intelligence evolution, relativistic temporal structure, and quantum entanglement phenomena. Quantum vacuum—far from representing absolute emptiness—exhibits continuous zero-point energy fluctuations generating virtual particle-antiparticle pairs via Heisenberg uncertainty principle, with Casimir effect providing experimental verification through measurable attractive force (F/A = -ℏcπ²/240d⁴) between conducting plates. Schrödinger's cat paradox illustrates quantum superposition collapse upon measurement, revealing observer-dependent reality contradicting classical determinism and motivating interpretational frameworks including Copenhagen collapse, many-worlds branching, and decoherence mechanisms. Binary computation architecture—utilizing base-2 representation (0,1 states)—exploits transistor switching characteristics enabling universal information encoding, with von Neumann architecture establishing stored-program paradigm foundational to modern computing. Artificial intelligence evolved from Turing's universal computation and symbolic reasoning systems through connectionist neural networks to contemporary deep learning architectures achieving superhuman performance in pattern recognition, natural language processing, and strategic game-playing domains. Einstein's special relativity demonstrates temporal relativity through velocity-dependent time dilation (τ = τ₀√(1-v²/c²)) and general relativity's gravitational time dilation near massive objects, with GPS satellite corrections providing daily experimental confirmation. Quantum entanglement—non-local correlation between spatially separated particles violating Bell inequalities—enables quantum information protocols including quantum cryptography, quantum teleportation, and quantum computation while challenging classical notions of locality and realism. The synthesis reveals deep connections: quantum vacuum provides cosmological initial conditions for universal genesis; measurement problem connects consciousness to physical reality; binary architecture enables AI substrate; relativistic effects constrain information transmission; and entanglement enables novel computational paradigms transcending classical limits.
Ontological Resolution Theory (ORT v2.0) — Priority Research Note "Decoherence is not environmental thermal noise: it is an unscheduled commit storm driven by vacuum packet contention.A qubit is not a trapped baryonic particle: it is an uncommitted sub-register in the shared topological carrier.Sever external port routing (k_trans = 0) — and unitary coherence becomes an invariant machine ground state." Current implementations of quantum processors (NISQ paradigm: superconducting transmons, trapped ions, quantum dots) suffer from an intractable decoherence barrier. We demonstrate that this failure stems directly from an ontological category error: treating baryonic defects (W → K_cell) within a continuous metric background as fundamental information carriers. In Ontological Resolution Theory (ORT v2.0), baryonic matter is an extreme computational bottleneck (ρ_c → 0) under permanent transaction pressure from the surrounding Floor 0 vacuum graph. Environmental decoherence is rigorously derived as an unscheduled interrupt stream (Γ_dec ∝ ||∇ρ_c||) forced onto the register by open coordinate transport ports (k_trans > 0). We formulate the complete architectural specification of a Native Floor 0 Quantum Machine (Q-MACH). Instead of physical cooling in metric space, quantum memory is realized as an isolated topological sub-graph bounded by an absolute zero-transmissivity barrier (k_trans = 0, k_int = 12). Under MDE Branch 1 evolution over 𝔽₂, such an isolated sub-register preserves its phase-space volume identically (det M = 1), eliminating decoherence at any ambient interface temperature. Quantum gates are implemented without analog field pulses via the Port Switching Protocol (PSP), which dynamically modulates boundary port conductance for discrete tick intervals Δn. Controlled state readout is achieved via parity projection (popcount(s) mod 2). This framework eliminates the need for geometric quantum error correction, replacing probabilistic wave mechanics with deterministic, reversible register microcode. Legal & Priority Notice: This publication establishes strict scientific and architectural priority for the topological port-switching quantum computing architecture on discrete carrier substrates under CC-BY-NC-ND 4.0.
The study of geometric tensors and their topological properties has emerged as a significant area within advanced mathematics and physics, offering potential for novel computational paradigms. This paper investigates the application of topological structure-based methods to geometric tensors, aiming to design a quantum computing acceleration paradigm. Specifically, we explore a novel approach to represent and manipulate geometric tensors through a topological structure, and propose a new quantum algorithm predicated on this structure. The core mechanism centers on introducing a topological structure onto the tensor, allowing for efficient optimization and simulation. The potential for quantum acceleration stems from exploiting the inherent properties of topological spaces and the ability of quantum algorithms to explore complex geometric spaces. This research contributes to the development of more efficient and robust computational methods, and highlights the synergistic relationship between topological structures and quantum computation. Furthermore, we analyze the implications of this approach for various geometric manipulation tasks, including optimization problems and simulation of complex physical systems. The proposed quantum algorithm utilizes the topological structure to guide the computation, achieving significant speedups compared to classical methods. The work offers a novel perspective on utilizing topological structures to enhance quantum computing, with implications for diverse mathematical and physical applications. Ultimately, this paper presents a framework for constructing quantum algorithms that benefit significantly from the unique properties of geometric tensors, demonstrating the potential for quantum computation to surpass classical approaches in certain complex scenarios. This investigation focuses on the core mechanism of representing geometric tensors using topological structures, and explores how this structure can be leveraged to accelerate computations.
Quantum Artificial Intelligence (Quantum AI) embodies the integration of quantum computational paradigms with artificial intelligence frameworks to address the computational intractability and scalability constraints inherent in classical AI systems. By leveraging quantum mechanical properties such as superposition, entanglement, and quantum interference, Quantum AI enables enhanced representation learning, accelerated optimization, and improved probabilistic inference in high-dimensional problem spaces. In parallel, deep-tech innovations—including advanced deep learning architectures, neuromorphic computing, and edge-based intelligent processing—are redefining the architectural foundations of next- generation intelligent systems through energy-efficient, adaptive, and real-time computation. This paper presents a technically rigorous and comprehensive review of Quantum AI and deep-tech innovations, focusing on algorithmic formulations, architectural models, and system-level integration strategies. Core methodologies such as quantum machine learning algorithms, parameterized quantum circuits, variational quantum algorithms, and hybrid quantum–classical optimization frameworks are critically analysed with respect to computational complexity, repressibility, and feasibility on noisy intermediate-scale quantum (NISQ) hardware. Additionally, the role of neuromorphic computing in enabling spiking neural architectures and event-driven processing is examined as a complementary paradigm to quantum-enhanced learning models, particularly for low-power and latency-critical applications. The paper further investigates application- driven deployments of Quantum AI across domains including medical diagnostics, cryptographic security, autonomous decision-making, and smart cyber-physical systems, highlighting performance trade-offs and implementation constraints. Key challenges such as quantum noise, decoherence, data encoding bottlenecks, limited qubit connectivity, and ethical governance are systematically discussed. Finally, future research directions are identified, emphasizing fault-tolerant quantum learning architectures, scalable hybrid integration with deep-tech systems, and co-design methodologies for realizing practical next-generation intelligence platforms.