Evolution of a two-dimensional quantum cellular neural network driven by an external field

A model of a two-dimensional quantum cellular neural network (QCNN) is pres ented in this article. The eigenvalues and eigenvectors for the Hamiltonian of a cell (neuron) are obtained, and we confirm that the ground or memory states are approximately two polarization states of 16 possible states in a cell (neuron) only when electron tunneling is relatively weak compared wit h the Coulomb repulsion. The evolution of the QCNN driven by a local extern al magnetic field is studied by solving the Liouville equation of the corre sponding two-dimensional Ising model. The formula for the evolution of the density operator is given by using a subdynamics approach. We show that the local external magnetic field can drive the system to a global polarizatio n state and induce a dynamical response in the original QCNN. This dynamica l response can be interpreted as a computable function and measured by the system output. (C) 1999 American Institute of Physics. [S0021-8979(99)07604 -5].