Investigation of the correlated dynamics of quantum-dot cellular automata circuits and systems

Quantum-dot Cellular Automata (QCA) provides a basis for classical computation without transistors. Many simulations of QCA rely upon the Intercellular Hartree Approximation (ICHA), which neglects the possibility of entanglement between cells. While simple and computationally efficient, the ICHA’s many shortcomings make it difficult to accurately model the dynamics of large systems of QCA cells. On the other hand, solving a full Hamiltonian for each circuit, while more accurate, becomes computationally intractable as the number of cells increases. This work explores an intermediate solution that exists somewhere in the solution space spanned by the ICHA and the full Hamiltonian. The solution presented in this thesis builds off of the work done by Toth et al., and studies the role that correlations play in the dynamics of QCA circuits. Using the coherence-vector formalism, we show that we can accurately capture the dynamical behaviour of QCA systems by including two-cell correlations. In order to capture the system’s interaction with the environment, we introduce a new method for computing the steady-state configurations of a QCA system using well-known stochastic methods, and use the relaxation-time approximation to drive the QCA system to these configurations. For relatively-low temperatures, we show that this approach is accurate to within a few percent, and can be computed in linear time. QCADesigner, the de facto simulation tool used in QCA research, has been used and cited in hundreds of papers since its creation in 2004. By implementing computationally accurate and efficient algorithms to the existing simulation engines present in QCADesigner, this research is expected to make a significant contribution to the future of QCA circuit design. In particular, researchers in the field will be able to identity a whole new set of design rules that will lead to more compact circuit design, realistic clocking schemes, and crosstalk-tolerant layouts. In addition, proper estimates on the power dissipation, pipelining, and limitations of room temperature operation will now be feasible for QCA circuits of any size; a huge step forward for QCA design.Applied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat