In this study, we explore the use of molecules and molecular electronics for quantum
computing. We construct one-qubit gates using one-electron scattering in molecules and two …

In the age of the post-Moore era, the next-generation computing model would be a hybrid
architecture consisting of different physical components, such as photonic chips. In 2008, it …

An explicit formula for the wave operators associated with Schrödinger operators on the
discrete half-line is deduced from their stationary expressions. The formula enables us to …

We prove Levinson's theorem for scattering on an (m+n)-vertex graph with n semi-infinite
paths each attached to a different vertex, generalizing a previous result for the case n= 1 …

The negative-AND (NAND) gate is universal for classical computation making it an important
target for development. A seminal quantum computing algorithm by Farhi, Goldstone and …

This paper proves new results on spectral and scattering theory for matrix-valued
Schrödinger operators on the discrete line with non-compactly supported perturbations …

We consider the Schrödinger operator on a star shaped graph with n edges joined at a
single vertex. We derive an expression for the trace of the difference of the perturbed and …

Determining properties of molecules and materials is one of the premier applications of
quantum computing. A major question in the thesis is: how might we use long-and near-term …

Certain continuous-time quantum walks can be viewed as scattering processes. These
processes can perform quantum computations, but it is challenging to design graphs with …

Utilizing discrete-time and continuous-time quantum walks, we propose a quantum random
access memory (qRAM) defined on a full binary tree. Our qRAM comprises 2n memory units …