Using the full quantum basis set to simulate quantum-dot cellular automata devices

摘要

Quantum-dot cellular automata (QCA) are a leading example of field-coupled nanocomputing (FCN) devices. All FCN devices rely on local field interactions among nanoscale building blocks that are arranged in patterns to perform useful calculations. Many methods have been introduced to simulate these devices, but not all of those methods are guaranteed to give correct results. The only method that is certain to give the correct results is constructing and diagonalizing the Hamiltonian operator using a full-basis set for the entire device. Not only does this give all stable states of the device (necessarily including the ground state), it also allows the detection of non-polarized states of QCA and other FCN cells. Unfortunately, simulating moderately complex devices using the full-basis set has been prohibitively expensive, both in storage space and in calculation time. The authors present a new method for calculating the eigenstates of a full-basis set Hamiltonian and use this method to demonstrate that at least one previously published QCA device does not, in fact, operate as it was simulated and described in the previous work. Identifying an error in a previously published device using a heretofore computationally infeasible simulation shows the value of using the exact full-basis calculation in the simulation of QCA devices.