# MAGNETISM AND QUANTUM COMPUTATION

## Learning outcomes of the course unit

Knowledge and understanding:

The aim of this course is to provide the basic theoretical knowledge on several aspects in quantum magnetism and the basic notions of quantum computation. The most important physical theories will be studied in terms of logical and mathematical structure, of experimental evidences and physical phenomena.

Applying knowledge and understanding:

The student will achieve the capability to apply these notions to analyze magnetic phenomena and interpret them on the basis of the mathematical formulation of the physical laws. In addition, the student will obtain basic competences in quantum computation.

Making judgments:

By the end of the course, the student should be able to understand the physical phenomena related to quantum magnetism and quantum information.

Communication skills:

The student must be able to clearly present the basic concepts of quantum magnetism and their consequences on observable phenomena. In addition, he must be able to discuss the basic concepts underlying quantum computation.

Learning skills:

The student should have acquired the learning skills related to magnetism and quantum computation, which are necessary to undertake successive studies with a high degree of autonomy.

## Prerequisites

Basic notions in Physics of Matter, Quantum Mechanics and Statistical Physics are required.

## Course contents summary

The course is divided into two parts: the first part deals with several aspects in quantum magnetism, while the second part is focused on the basis of quantum computation. In particular, the lectures cover the following subjects:

-Crystal-field theory.

-Irreducible tensor operators.

-Direct exchange interaction-RKKY interaction-Superexchange interaction.

-Magnetic molecules-Strong exchange limit.

-Mean field theory in magnetic materials-Spin waves.

-Hubbard model-Stoner model.

-Kubo formula-Green functions.

-Quantum algorithms-Single and two qubit quantum gates-Quantum Simulators-Entanglement-Quantum computation with Molecular Nanomagnets

## Recommended readings

-Condensed Matter Physics by M. P. Marder, Wiley.

-Quantum Theory of Magnetism by W. Nolting and A. Ramakanth, Springer.

-Lecture Notes on Electron Correlation and Magnetism by P. Fazekas, World Scientific.

-Quantum Computation and Quantum Information by M.A. Nielsen and I.L. Chuang, Cambridge.

## Teaching methods

Slides, blackboard calculations and numerical simulations.

## Assessment methods and criteria

The evaluation is based on an oral test whose aim is to verify the student’s knowledge and his ability to apply and connect the concepts. The first part of the test is the discussion of a topic chosen by the student, while the second part contains questions on other topics of the course. The first part has a weight of about 1/3 in the final evaluation.

The evaluation is on a scale of 30 (cum laude for a perfect test) and the duration of the oral test is about one hour. The online registration is compulsory.