#### LTAT.00.015 "Book Course" 6 ECTS

*"Fermions"* — Electronic Structure

**Note**

*not*through ÕIS.

In this course, students will learn the mathematical foundations of electronic structure theory: The quantum mechanics of molecules and materials in the Born-Oppenheimer approximation. There is a heavy focus on the concepts that are exploited in quantum algorithms for *ab initio* computational physical chemistry (molecules) and computational materials (condensed matter).

At school, you already learned about the structure of electrons in molecules: They form clouds, you only need the "outer" ones — what else is there to know? While for some computations and simulations quantum-agnostic techniques suffice, for others they don't, particularly. It is mind-numbing, for example, that enzyme nitrogenase can transform N₂ (atmospheric nitrogen) into NH₃ (ammonia) with essentially no energy used — but we humans are not able to understand WTF that shitty little enzyme is exactly doing, and consequently have to spend 1-2% of all our energy on our process for it (for making fertilizer). Via fault-tolerance, quantum computing devices with a minimum of hardware characteristics (number of qubits, connectivity, noise model, nose parameters, gate times) have proven in simulations and on paper to be able to simulate electronic structure in the key molecules at work in nitrogenase. Many more processes in molecules thus elude our understanding of their workings and hence our ability to imitate them. The capacity to perform computer simulations of molecules and materials — whether they appear in nature or not — on the quantum level to predict their properties is *the* valuable application of quantum computers. (Unless you want to count using Shor's algorithm to read someone else's emails, of course.)

#### Very preliminary syllabus

- Let's start with something fun: Fermionic algebra
- Fock space
- Coulomb Hamiltonian; Born-Oppenheimer
- From 1st to 2nd quantization
- Basis changes and Givens rotations
- Hartree-Fock theory
- Few-particle reduced density matrices

#### Requirements

- MTAT.05.008
- MTAT.07.024 (mixed states)
- QIP
*Light*

If you want, just as QIP *Light* was about bosons (photons and phonons), this course is about electrons (fermions), hence the short name.

#### Course Organization

This is a "Reading Course" meaning that the students mostly read independently material prepared by the instructor; in theory courses (generally speaking) there should be exercises for students to solve. Difficulties encountered with the reading material as well as the solutions to the exercises are discussed in meetings with other students and the instructor.

For this course, textbooks are outdated while original research is too difficult or spread over dozens of papers. Hence, the reading material for this course will be created by the instructor from scratch, in parallel to the course.

There will probably be some kind of entry exam to check the math background.

Instructor:

- Assoc Prof Dirk Oliver Theis