Implementation of multivariable logic functions in parallel by electrical addressing a molecule of three dopants in Silicon

To realize low power compact logic circuits one can explore parallel operation on single nanoscale devices. An added incentive is to use multivalued (as distinct from Boolean) logic. Here we theoretically demonstrate that the computation of all the possible outputs of a multivariate, multivalued logic function can be implemented in parallel by electrical addressing of a molecule made up of three interacting dopant atoms embedded in Si. The electronic states of the dopant molecule are addressed by pulsing a gate voltage. By simulating the time evolution of the non stationary electronic density built by the gate voltage, we show that one can implement a molecular decision tree that provides in parallel all the outputs for all the inputs of the multivariate, multivalued logic function. The outputs are encoded in the populations and in the bond orders of the dopant molecule, which can be measured using a STM tip. We show that the implementation of the molecular logic tree is equivalent to a spectral function decomposition. The function that is evaluated can be field-programmed by changing the time profile of the pulsed gate voltage.