Mathematical approaches for characterization, control, calibration and validation of a quantum computing device

TL;DR

This paper provides a comprehensive case study on the mathematical modeling, calibration, control, and validation of a quantum computing device, aimed at helping newcomers understand the entire process from theory to experiment.

Contribution

It introduces a detailed methodology combining experimental and mathematical techniques for quantum device characterization and control, filling a gap in existing literature.

Findings

Successful characterization and control of a qudit device at LLNL

Validation of optimized control pulses through experiments

Integration of mathematical models with experimental procedures

Abstract

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.