Hamiltonian-based qutrit quantum neural network with multi-subspace feature map

We present QNN-3L, a quantum neural network architecture based on three-level systems (qutrits) with longitudinal Ising-type couplings on a one-dimensional lattice. Starting from an explicit phenomenological multilevel Hamiltonian that includes local anharmonicity, diagonal couplings and resonant control pulses, we derive native selective rotations on computational subspaces and a nearest-neighbour controlled-\((Z)\) primitive. We prove that these native operations generate a subgroup dense in \((\mathrm{SU}(3^N))\), providing approximate universality. To introduce effective nonlinearity while preserving coherent unitary propagation, we propose a hybrid architecture that uses a multi-subspace feature map: classical inputs are encoded via sequential rotations on two independent qutrit subspaces, whose non-commutativity enriches the implicit quantum kernel. We perform ablation studies and kernel diagnostics showing that the multi-subspace encoding yields improved kernel separation and more stable training than single-subspace alternatives. Numerical benchmarks for \((N=3)\)–6 qutrits (dimension \((\dim\mathcal{H}\leq729)\)) demonstrate comparable expressibility at depths \((L\ge3)\) and enhanced shallow-circuit entangling power relative to equivalent qubit circuits, and validate proof-of-concept supervised learning on a canonical nonlinear task. MSC Classification: 03.67.Ac , 03.67.Lx , 07.05.Mh