### Sciences

## Subject: QUANTUM INFORMATION PROCESSING (A.A. 2020/2021)

### master degree course in PHYSICS – FISICA

Course year | 1 |
---|---|

CFU | 6 |

Teaching units |
Unit Quantum Information Processing
Microphysics and Material Structure (lesson)
- TAF: Compulsory subjects, characteristic of the class SSD: FIS/03 CFU: 6
Paolo BORDONE |

Exam type | oral |

Evaluation | final vote |

Teaching language | English |

### Teachers

### Overview

Knowledge and understanding:

At the end of the course the student will acquire knowledge of the basic concepts of quantum information theory and of some fundamental algorithms of quantum computation theory.

Applying knowledge and understanding:

At the end of the course the student will have the conceptual tools necessary to independently deal with the fundamental aspects of quantum information theory, and to independently study the original literature on the subject.

Making judgements:

At the end of the course the student will be able to independently evaluate how to deal with a problem in the fields of quantum information theory.

Communicating skills:

At the end of the course the student will be able to write reports on the subject treated in the course and to discuss them with appropriate technical language.

Learning skills:

The study, entirely carried out in English, will allow the development of autonomous learning skills on topics related to those developed in the course, and it prepares the student for doing active research in this area.

### Admission requirements

Knowledge of quantum mechanics at bachelor's degree level.

### Course contents

Definition of quantum bit (qubit), quantum gates and quantum circuits. The density matrix and its representations. The entanglement: the Bell's inequalities and entanglement quantification. Entanglement as a resource for quantum communication. Teleportation and dense coding. Generalized quantum dynamics as a generalization of the standard unitary evolution of quantum states. Quantum maps and their Kraus representation. The no-cloning theorem. Positive operator valued measures (POVMs) as a generalization of the standard projective measurements, Naimark's theorem. Quantum cryptography. Quantum algorithms: the Deutsch algorithm, the Grover search algorithm.

### Teaching methods

Lectures. Lessons will normally be conducted remotely asynchronously (recorded) due to the COVID19 health situation. Working students who can not attend regular classes should contact the teacher to get informations about the study program, about the suggested textbooks and to establish the way to access the final oral examination. Office hours: Wednesday and Thursday from 3 p.m. to 4 p.m, or by e-mail appointment.

### Assessment methods

The evaluation of is made by oral examination with questions on all the main parts of the program: ranging from the definition of logic gates to the density matrix. From the Bell's inequalities to entanglement quantification. From the generalisation of quantum dynamics to the quantum maps. From the measurements problem to quantum cryptography, up to some fundamental algorithms for quantum computing. The exam tests could be carried out in the presence or at a distance depending on the evolution of the COVID19 situation.

### Learning outcomes

Knowledge and understanding:

At the end of the course the student will acquire knowledge of the basic concepts of quantum information theory and of some fundamental algorithms of quantum computation theory.

Applying knowledge and understanding:

At the end of the course the student will have the conceptual tools necessary to independently deal with the fundamental aspects of quantum information theory, and to independently study the original literature on the subject.

Making judgements:

At the end of the course the student will be able to independently evaluate how to deal with a problem in the fields of quantum information theory.

Communicating skills:

At the end of the course the student will be able to write reports on the subject treated in the course and to discuss them with appropriate technical language.

Learning skills:

The study, entirely carried out in English, will allow the development of autonomous learning skills on topics related to those developed in the course.

### Readings

J.A. Bergou and M. Hillery: "Introduction to the theory of quantum information processing", Springer.

V. Vedral: "Introduction to quantum information science", OXFORD University Press.

N.D. Mermin: "Quantum computer science", CAMBRIDGE University Press.

J. Preskill. "Lecture Notes for Physics 229: Quantum information and computation", http://www.theory.caltech.edu/people/preskill/ph229/

G. Benenti, G. Casati, D. Rossini, G. Strini: "Principles of quantum computation and information", World Scientific.