Physical Sciences and Mathematics Commons^™

Methodologies For Quantum Circuit And Algorithm Design At Low And High Levels, Edison Tsai

Dissertations and Theses

Although the concept of quantum computing has existed for decades, the technology needed to successfully implement a quantum computing system has not yet reached the level of sophistication, reliability, and scalability necessary for commercial viability until very recently. Significant progress on this front was made in the past few years, with IBM planning to create a 1000-qubit chip by the end of 2023, and Google already claiming to have achieved quantum supremacy. Other major industry players such as Intel and Microsoft have also invested significant amounts of resources into quantum computing research.

Any viable computing system requires both hardware and …

Quantum Field Theories, Topological Materials, And Topological Quantum Computing, Muhammad Ilyas

Dissertations and Theses

A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with the environment. It is a real challenge to completely isolate a quantum system to make it free of decoherence. This problem can be circumvented by the use of topological quantum phases of matter. These phases have quasiparticles excitations called anyons. The anyons are charge-flux composites and show exotic fractional statistics. When the order of exchange matters, then the anyons are called non-Abelian anyons. Majorana …

A Method For Achieving Analytic Formulas For Three Body Integrals Consisting Of Powers And Exponentials In All Three Interparticle Hyllerass Coordinates, Chris M. Keating

Dissertations and Theses

After an introduction to the variational principle of three body systems via the Helium atom, we present general analytical formulas for the radial parts of integrals that occur when three body systems are described using wave functions that consist of powers and exponentials in all three interparticle Hylleraas coordinates [Hylleraas1929]. This work is an extension of integrals given by Harris, Frolov and Smith, Jr. [Harris2004]. Specifically included are radial integrals encountered in calculations involving the dipole moment matrix element in Hylleraas coordinates that contain a function f(kr₁) (such as a spherical Bessel function) in addition to …