Module overview
This course has two related parts: Electronic Structure Theory and Quantum Optimal Control. Through 24 lectures, students will gain in-depth knowledge of computational techniques and quan-tum control methods essential for advanced work in quantum technology engineering.
Part 1: Electronic Structure Theory
This part begins with an overview of the anatomy of a modern supercomputer, essential for under-standing the computational background of electronic structure calculations. Following this, stu-dents will learn about electronic structure theory software and visualization tools, crucial for practi-cal applications in the field.
The course progresses to cover methods and terminology central to electronic structure theory, in-cluding Hartree-Fock/Self-Consistent Field (SCF) methods, basis sets, semi-empirical methods, Møller–Plesset perturbation theory (MPn), Configuration Interaction (CI), Multi-Configurational Self-Consistent Field (MCSCF), and Coupled Cluster (CC) theory. A dedicated lecture on Density Functional Theory (DFT) will further expand students' understanding of computational methods.
Practical aspects such as molecular geometry optimization, Z-matrices, and periodic boundary con-ditions (PBCs) are addressed next, followed by lectures on Newtonian and Born-Oppenheimer mo-lecular dynamics. The course then delves into various property calculations, exploring linear re-sponse theory, time-dependent SCF, and calculations of energies, gradients, frequencies, polarizabili-ties, solvent effects, band structures of periodic solids, and magnetic interaction tensors.
Part 2: Quantum Optimal Control
This part begins with an exploration of the time-dependent Schrödinger equation and density opera-tor formalism, laying the groundwork for understanding quantum control.
Subsequent lectures introduce the control channels of quantum devices and foundational concepts in theoretical mechanics and optimization, including Lagrangians, calculus of variations, and Pontryagin’s maximum principle. Students will then explore key themes in quantum control such as controllability, reachability, and the Krotov method, including its derivation and applications.
The course continues with an examination of Gradient Ascent Pulse Engineering (GRAPE), a pivotal technique in quantum control, covering both its theoretical underpinnings and applications. This is complemented by a lecture on the numerical implementation of optimal control algorithms, provid-ing practical skills for computational applications.
The course concludes with a focus on the applications of quantum optimal control in spin systems, demonstrating the relevance of these techniques in practical quantum technologies.
By the end of this course, students will have a good understanding of theoretical and computational aspects of electronic structure theory and quantum optimal control, and the skills to contribute to research and development in quantum technologies.