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Bulletin of the American Physical Society

Quantum Method for Fault Tolerance Calculations in Quantum-dot Cellular Automata Clocked Devices

Ioan Sturzu, Mahfuza Khatun

Published Mar 25, 2005• 0 citations
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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.

•Jan 1, 2020•0 citations
We present a numerical study of fault tolerance properties in quantum-dot cellular automata (QCA) devices. A full-basis quantum method is used for calculations of the Hamiltonian, and a statistical model has been introduced to simulate the influence of position defects of the dots within cells on the logical output. Combined effects of temperature and cell defects on a shift register have been studied. Uniform and normal distributions have been used for the cell defect simulations. Normal distribution simulations produce realistic results compared to the uniform distribution. In order to show the operational limit of a device, parameters such as “displacement factor” and “success rate” are introduced. Results show that the fault tolerance of a QCA device is strongly dependent on temperature as well as on the cell defects. The robustness of a shift register is also dependent on the size of the device.
Molecular quantum-dot cellular automata (QCA) may provide low-power, high-speed computational hardware for processing classical information. Simulation and modeling play an important role in the design of QCA circuits because fully coherent models of QCA scale exponentially with the number of devices, and such models are severely limited in size. For larger circuits, approximations become necessary. In the era of fault-tolerant quantum computation, however, it may become possible to model large QCA circuits without such limitations. This work explores the use of the noisy-intermediate scale quantum (NISQ) variational quantum eigensolver (VQE) method for estimating the ground state of QCA circuits. This is relevant because the computational result of a QCA calculation is encoded in the circuit’s ground state. In this study, VQE is used to model logic circuits, including binary wires, inverters, and majority gates. VQE models are performed by ideal simulators, noisy simulators, and actual quantum hardware. This study demonstrates that VQE may indeed be used to model molecular QCA circuits. It is observed that using modern NISQ hardware, results are still quite sensitive to noise, so measures should be taken to minimize noise. These include simplifying the ansatz circuit whenever possible and using low-noise hardware.
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.