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

M I Aksman

Mikhail I Aksman

M I Aksman

Michael I Aksman

We present an explicit algorithmic realization of quantum computation on a finitespectral manifold of dimension N = 861 using the KAN–DAM architecture. Logical states areencoded nonlocally across all modes, and evolution proceeds through repeated nonlineartransformations followed by a deterministic projection onto the constrained manifold. Thismechanism supplies intrinsic error suppression and state-independent dynamics withoutrequiring external error-correcting codes or precise gate calibration. We detail the update rule,prove universality through functional approximation and nonlinear coupling, compare theapproach to tensor-network methods and adiabatic quantum computing, and provide a minimalsimulation protocol that can be implemented immediately on classical hardware. The result is acomputational paradigm in which logic, error correction, and thermodynamic consistency allemerge naturally from projection onto a finite-capacity spectral structure.

Chien‐Hung Cho, Chih-Yu Chen, Kuo-Chin Chen +6 more

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.