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KAN-DAM Quantum Computing: Algorithm, Operator Foundations, and Rigorous Simulation on the 861-Node Spectral Manifold

Mikhail I Aksman

Published Oct 14, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.19551.01446

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We present a rigorous head-to-head analytical comparison between the KAN-DAM (KolmogorovArnold Network + Dense Associative Memory) architecture operating on a xed nite spectral manifold (N = 861) and conventional tensor-network (TN) methods. Tensor networks suer exponential scaling with bond dimension due to volume-law entanglement generation, and their exact contraction in 2D/3D is strictly #P-hard, forcing systematic topological destruction via Singular Value Decomposition (SVD) truncation. Conversely, KAN-DAMmaintains a xed dimensionality N, achieves a bounded per-step complexity of O(N2) and total cost O(N2T), and suppresses non-physical errors globally via Dense Associative Memory geometric projection rather than truncation. The Kolmogorov-Arnold representation guarantees dense functional expressivity without requiring explicit, localized entanglement management. This establishes KAN-DAM as a bounded-cost, geometrically stabilized computational paradigm ideally suited for non-perturbative problems whose physics is constrained to a low-dimensional topological surface.

•Jun 18, 2026•0 citations
The KAN-DAM computing architecture establishes a deterministic quantum-computational model hosted on a finite 861-node spectral manifold, replacing isolated physical qubits and discrete gate sequences with globally distributed, non-local state representations. Information processing advances through an alternating cycle of linear functional mode mixing, non-linear dense associative coupling, and immediate geometric projection back onto the constrained manifold. The system integrates global Chebyshev spectral polynomial expansions with localized adaptive spline representations, coupling macro-level coherence with localized gradient absorption to eliminate oscillatory instabilities. The non-linear stage generates many-body interactions and effective entanglement in a single transformation without requiring deep sequences of two-qubit operations. Error suppression operates as an automatic geometric filter rather than an active algorithmic routine: perturbations that drift outside the rigid manifold constraints are discarded by the projection step, eliminating the need for ancilla qubits or syndrome measurements. This design circumvents the exponential entanglement scaling limits of classical tensor networks and the critical gap-closing slowdowns of adiabatic quantum annealing, providing an inherently stable platform that can be simulated classically or implemented across photonic, superconducting, and cold-atom hardware.
We present a rigorous head-to-head analytical comparison between the KAN-DAM (KolmogorovArnold Network + Dense Associative Memory) architecture operating on a xed nite spectral manifold (N = 861) and conventional tensor-network (TN) methods. Tensor networks suer exponential scaling with bond dimension due to volume-law entanglement generation, and their exact contraction in 2D/3D is strictly #P-hard, forcing systematic topological destruction via Singular Value Decomposition (SVD) truncation. Conversely, KAN-DAMmaintains a xed dimensionality N, achieves a bounded per-step complexity of O(N2) and total cost O(N2T), and suppresses non-physical errors globally via Dense Associative Memory geometric projection rather than truncation. The Kolmogorov-Arnold representation guarantees dense functional expressivity without requiring explicit, localized entanglement management. This establishes KAN-DAM as a bounded-cost, geometrically stabilized computational paradigm ideally suited for non-perturbative problems whose physics is constrained to a low-dimensional topological surface.