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Energy spectra informed performance of clocked quantum-dot cellular automata Retallick, Jacob


Understanding the dynamic behaviour of nanoscale quantum-dot cellular automata (QCA) networks involves the simulation of large numbers of QCA devices, with the complexity of the full quantum treatment exponential in the network size. Previous attempts to limit this complexity introduce simplifying assumptions with known inaccuracies. In this thesis we investigate an alternate approach, extracting performance metrics through analysing the low energy eigenspectrum of a clocked network. We make two major contributions. In the first part of this thesis, we study the use of silicon dangling bonds (SiDBs) as a platform for combinatorial logic, and ultimately nanoscale QCA. We present models for understanding the preferred configurations and dynamics of charges in these structures. We consider the clocking of SiDB-based QCA wires, and reveal a complicated trajectory of charge states that serve as a challenge for QCA operation. By studying SiDB-based QCA from the framework of the familiar 3-state model, in which these preferred charge states translate to eigenstates of a system Hamiltonian, we determine conditions for which SiDB-QCA wires can cor- rectly operate when clocked. These conditions are potentially impractical unless net-neutral SiDB arrangements can be achieved. The remaining bulk of the thesis revolves around the link between QCA clocking and quantum annealing. We first investigate the adiabaticity of simple 2-state QCA networks under zone clocking. We present upper bounds on the clocking frequency beyond which adiabaticity falls below a 99% threshold, and demonstrate how we can efficiently estimate clocking performance using only a few of the energy eigenstates. Due to a natural mapping between QCA cells and superconduct- ing flux qubits, the potential for investigating performance using a physical quantum annealer is explored. Methods for embedding QCA networks onto the annealer are discussed and a selection of annealing results are analyzed. Finally, we establish a method for decomposing the system Hamiltonian into contributions from given components, and a means to identify meaningful components which critically affect clocking performance. This framework reveals a heuristic algorithm for approximating the low energy eigenspectra of large QCA networks, enabling future investigations into the performance of networks well beyond previous size limitations.

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