Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Kolmogorov-Arnold Networks on the 861-Node Heegner-Rigid Spectral Manifold Quantum Computing Algorithm, Simulation, and Engineering Realization on a Finite Arithmetic Lattice

Michael Aksman

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.14948.95367

Related papers

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

Mikhail I Aksman

•Oct 14, 2026•0 citations

KAN-DAM QUANTUM COMPUTING: ALGORITHM AND SIMULATION ON THE 861-NODE SPECTRAL MANIFOLD

Mikhail I Aksman

•Jan 1, 2026•0 citations

Adaptive Quantum-Inspired Kolmogorov-Arnold Networks for Dynamic Grid-Based Computations

Siddarth Laxminarayanan

•Feb 9, 2026•0 citations

KAN-DAM Cryptographic Trapdoors on the DSM-861

Michael I Aksman

We present a complete cryptographic trapdoor primitive constructed by embeddingKolmogorov–Arnold Networks (KAN) with Dense Associative Memory (DAM) layersonto the DSM-861 Deterministic Spectral Manifold — a rigid triangular-lattice 3-toruswith exactly N = 861 nodes, 72-fold gear-lock symmetry, topological defect δ = -1/24,and intrinsic Casimir residue |ε| = 1/12 (derived via Euler-Maclaurin regularization ofδ). The private key is an exact initial spectral signature ψ0. Forward trapdoor evaluation (private key → public key) is an exact algebraic spectral mapping of the Kolmogorov–Arnold decomposition executed via discrete Lax pairs satisfying the zero-curvature condition [∂/∂t − A, L] = 0. The Dense Associative Memory layerresolves superpositions deterministically. Inversion is rendered computationallyintractable by the non-periodic, non-Abelian geometry of the closed manifold,topological phase locking, and intrinsic Casimir stabilization. This constructiondelivers deterministic, drift-free signature generation and verification with zeroprobabilistic failure. We provide full mathematical definitions, explicit constructions,rigorous security reductions, quantitative resource comparisons with Babbush et al.(2026), implementation considerations, and integration with intrinsic topologicalquantum error correction. The primitive offers a practical, quantum-resistantalternative to lattice-based post-quantum cryptography with dramatically reducedoverhead and no reliance on heuristic hardness assumptions.

•May 24, 2026•0 citations

KAN-DAM Quantum Computing on the 861-Node Spectral Manifold: Algorithmic Architecture, Non-Linear Dynamics, and Universal Hardware Realization

Michael Aksman

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.

•Nov 1, 2026•0 citations

QKAN: quantum Kolmogorov-Arnold networks with applications in machine learning and multivariate state preparation

Petr Ivashkov, Po‐Wei Huang, Kelvin Koor +2 more

We introduce quantum Kolmogorov-Arnold networks (QKAN), a quantum algorithmic framework inspired by the recently proposed Kolmogorov-Arnold Networks (KAN). QKAN inherits the compositional structure of KAN and is based on block-encodings, constructed recursively from a single layer using quantum singular value transformation. We demonstrate the algorithmic utility of QKAN in two applications. First, we introduce and analyze QKAN as a quantum learning model, treating the eigenvalues of block-encoded matrices as neurons and applying parametrized activation functions on the edges of the network. We show that QKAN is a wide-and-shallow neural architecture, where shallow depth is compensated by exponentially wide layers whenever efficient block-encodings of inputs are available. We further discuss how to parametrize and train QKAN using parametrized quantum circuits and quantum linear algebra subroutines. Second, we demonstrate that QKAN can serve as a multivariate quantum state-preparation protocol for functions with shallow compositional structure. We demonstrate this by efficiently preparing a multivariate Gaussian quantum state using a two-layer QKAN. Looking forward, we anticipate that QKAN's compositional and modular design will enable new applications in quantum machine learning and quantum state preparation.

arXiv:2410.04435•npj Quantum Information•Mar 11, 2026•4 citations
We present a complete cryptographic trapdoor primitive constructed by embeddingKolmogorov–Arnold Networks (KAN) with Dense Associative Memory (DAM) layersonto the DSM-861 Deterministic Spectral Manifold — a rigid triangular-lattice 3-toruswith exactly N = 861 nodes, 72-fold gear-lock symmetry, topological defect δ = -1/24,and intrinsic Casimir residue |ε| = 1/12 (derived via Euler-Maclaurin regularization ofδ). The private key is an exact initial spectral signature ψ0. Forward trapdoor evaluation (private key → public key) is an exact algebraic spectral mapping of the Kolmogorov–Arnold decomposition executed via discrete Lax pairs satisfying the zero-curvature condition [∂/∂t − A, L] = 0. The Dense Associative Memory layerresolves superpositions deterministically. Inversion is rendered computationallyintractable by the non-periodic, non-Abelian geometry of the closed manifold,topological phase locking, and intrinsic Casimir stabilization. This constructiondelivers deterministic, drift-free signature generation and verification with zeroprobabilistic failure. We provide full mathematical definitions, explicit constructions,rigorous security reductions, quantitative resource comparisons with Babbush et al.(2026), implementation considerations, and integration with intrinsic topologicalquantum error correction. The primitive offers a practical, quantum-resistantalternative to lattice-based post-quantum cryptography with dramatically reducedoverhead and no reliance on heuristic hardness assumptions.
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 introduce quantum Kolmogorov-Arnold networks (QKAN), a quantum algorithmic framework inspired by the recently proposed Kolmogorov-Arnold Networks (KAN). QKAN inherits the compositional structure of KAN and is based on block-encodings, constructed recursively from a single layer using quantum singular value transformation. We demonstrate the algorithmic utility of QKAN in two applications. First, we introduce and analyze QKAN as a quantum learning model, treating the eigenvalues of block-encoded matrices as neurons and applying parametrized activation functions on the edges of the network. We show that QKAN is a wide-and-shallow neural architecture, where shallow depth is compensated by exponentially wide layers whenever efficient block-encodings of inputs are available. We further discuss how to parametrize and train QKAN using parametrized quantum circuits and quantum linear algebra subroutines. Second, we demonstrate that QKAN can serve as a multivariate quantum state-preparation protocol for functions with shallow compositional structure. We demonstrate this by efficiently preparing a multivariate Gaussian quantum state using a two-layer QKAN. Looking forward, we anticipate that QKAN's compositional and modular design will enable new applications in quantum machine learning and quantum state preparation.