Hyper-connected Neural Networks as Topological Qubits Optimised with Narrow-Beam Quantum Confinement

Abstract

We introduce a novel algorithm in which a hyper-connected neural network acts as a distributed substrate encoding topological quantum information across its graph structure rather than in isolated physical qubits. The central claim is as follows: when the network’s complex-valued weight matrix is constrained to carry Aharonov-Bohm phases, its collective low-energy manifold reproduces the protected ground-space of a topological stabiliser code, without requiring any single node to sustain quantum coherence indefinitely. Decoherence is countered by a biologically-derived adaptive algorithm, transplanted from the vascular dynamics of Physarum polycephalum, which re-weights inter-node channels in real time by treating quantum mutual information as the analogue of nutrient flow. External confinement is provided by a focused Gaussian beam forming an optical dipole trap ,a quantum Faraday cage whose depth-to-temperature ratio η = U 0 /k B T ≈ 500 suppresses environmental coupling by three orders of magnitude relative to room-temperature operation. We derive the full network Hamiltonian from a transverse-field Ising graph model, compute its topological gap analytically, formulate the Lindblad master equation governing open-system evolution, and show that the slime-mould update rule drives the network toward a fixed point at which the logical error rate scales as p L ∝ ( p/p th ) ⌈d/2⌉ with effective distance d = ⌊ √ N⌋ for an N -node lattice. Numerical simulation across p ∈ [10 −3 , 10 −1 ] confirms that the hybrid scheme outperforms a standard distance-3 surface code below the common threshold p ≈ 10 −2 , while requiring N = 9 physical resources compared with d 2 = 9 physical qubits encoding a single logical qubit the same count but with an integrated noise-adaptive layer absent in the surface-code paradigm. We close with an honest accounting of where the framework rests on extrapolation and where experimental falsification is nearest.