We proposed new basic theory and methods for quantum computation and neuro-computer based on functional path integral of quantum theory. And then we concretely calculated probability amplitudes for quantum circuit and slit which have interferences and tunnel effects. We give operator expressions of switches and their circuits, and the diagrams of those systems correspond to potentials of Hamiltonian. Finally, we found that AND-circuit is represented by second order of perturbation, and OR-circuit looks upon as two particles scattering system. We showed it is useful to design and to make tests for new quantum system and computers.
