Quantum gauged neural networks: learning and recalling

We study quantum neural networks on a 3D lattice, which contain neuron variable S_x on each site and synaptic variables J_xμ(μ = 1,2,3) on each link. The networks have a local gauge symmetry, where J_xμ are regarded as gauge variables connecting nearest-neighbor sites. We simulate processes of learning a pattern of S_x and recalling it. The rate of recalling the pattern is calculated and compared for three cases, (I) classical (Hopfield-type) Z(2) model, (II) quantum U(1) Higgs model, (III) quantum CP1 + U(1) spin(qubit) model. The quantum effects are found to reduce the performance.