Implementation of a Simulation Engine for Clocked Molecular QCA

This paper presents the model and implementation of a new simulation engine, within the existing QCADesigner simulation tool, that will be used to simulate clocked molecular QCA cells and circuits. The clocking mechanism uses a layer of patterned electrodes to switch the cells by controlling the electrostatic potential energy of the different electronic configurations of the cells. The simulation engine models each QCA cell in the circuit using a three-state Hamiltonian. This Hamiltonian is projected onto a basis of generators of the special unitary group SU(3). The Bloch equation is solved to determine the time evolution of the coherence vector in this basis. Interaction with the environment is modelled using a density matrix approach and a relaxation-time approximation. We apply the Hartree-Fock approximation to model the interactions between cells that are assumed to be through expectation values in order to make the problem computationally feasible