Using simulation to assess the feasibility of quantum computing

Quantum computation is a new technology with the potential for providing exponential parallelism. The feasibility of a quantum computer is limited by two different types of errors, decoherence and inaccuracies. This dissertation uses simulation to investigate the feasibility of implementing one of the proposed realizations of a quantum computer, the trapped ion quantum computer. Because of the exponential complexity of a quantum computer, simulating one requires vast processing and memory resources. For this reason I develop several techniques to reduce the complexity of simulating a quantum computer. A parallel simulator is also used. Using the parallel simulator I am able to simulate circuits with close to 100,000 basic operations. The simulation studies show that the effectiveness of a quantum computer, without a mechanism for controlling errors, is severely limited. However the power of a quantum computer can be increased by using several techniques to mitigate the effects of error. Therefore a realizable quantum computer has three fundamental requirements: First, both hardware and software mechanisms must be used to correct errors as they occur. Second, the architecture of a quantum computer is very important; it must be designed to mitigate errors and it must be able to execute multiple operations in parallel. Last, quantum circuits must be constructed in an efficient manner, to minimize the total number of operations.