iii iv CHRISTOPHER L. DWYER: Self-Assembled Computer Architecture: Design and Fabrication Theory (under the direction of Russell M. Taylor) This dissertation explores the design and fabrication of massively-parallel computers using self-assembling electronic circuitry. A DNA-guided self-assembly method, inspired by discoveries in chemistry, materials science, and physics, is used to develop an argument for the feasibility of constructing complex circuitry. The fabrication yield of such a process is calculated. Together, these form the foundation for a discussion of the computer architectures and implementations that this self-assembling process enables. Simulations estimate the electrical performance of the components used in the self-assembly process. Traditional drift-diffusion simulations were used to evaluate a ring-gated field effect transistor and the results were applied to a circuit level simulation to evaluate

Abstract The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the Church-Turing hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinate-free mathematical language which is both constructive and non-local to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagram can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of Church-Turing and quantum theories. It has constructively to bridge the non-local chasm between the weak anticipation of mathematics and the strong anticipation of physics.