  Quantum computing has received significant amounts of interest from many
different research communities over the last few years. Although there are many
introductory texts that focus on the algorithmic parts of quantum computing,
there is a dearth of publications that describe the modeling, calibration and
operation of current quantum computing devices. One aim of this report is to
fill that void by providing a case study that walks through the entire
procedure from the characterization and optimal control of a qudit device at
Lawrence Livermore National Laboratory (LLNL) to the validation of the results.
A goal of the report is to provide an introduction for students and
researchers, especially computational mathematicians, who are interested in but
new to quantum computing. Both experimental and mathematical aspects of this
procedure are discussed. We present a description of the LLNL QuDIT testbed,
the mathematical models that are used to describe it, and the numerical methods
that are used to to design optimal controls. We also present experimental and
computational methods that can be used to characterize a quantum device.
Finally, an experimental validation of an optimized control pulse is presented,
which relies on the accuracy of the characterization and the optimal control
methodologies.
