Characterizing Quantum-Dot Cellular Automata

Abstract

We undertake an in-depth numerical study of quantum-dot cellular automata (QCA), a beyond-CMOS computing paradigm which represents bits as bistable charge distributions in cells consisting of quantum dots. Using semi-realistic but material-independent mod- elling, we characterize the building blocks of QCA circuits in as detailed and unbiased a manner as possible. Starting from an extended Hubbard model, and introducing two controlled Hilbert space truncations whose limits we study and understand, we use exact diagonalization to calculate time-independent properties of small systems. We derive a transverse-field Ising model as an effective description for QCA devices, but find that it is only valid in a restrictive parameter range. We demonstrate that the commonly used intercellular Hartree approximation is inadequate and gives results that are qualitatively incorrect. In contrast to previous work, we show that the response between pairs of ad- jacent cells is linear and does not exhibit gain. Non-linearity and gain only emerge in response to static-charge input cells that have no quantum dynamics of their own. As a consequence, QCA circuits cannot retain a logic state in the thermodynamic limit, and there is a maximum circuit size set by the system’s parameters. Overall, QCA as a com- puting architecture is seen to be more fragile than previously thought. We establish charge neutral cells as a strict requirement for QCA operation. We identify parameter bounds for functional devices: small cell-cell distances, moderate temperatures, and large Coulomb energy scales are necessary.