OVERVIEW

The aim of this course is to illustrate the basic principles of quantum computation and quantum information. The main experimental platforms where such quantum technologies are implemented will also be discussed.

AIMS AND CONTENT

LEARNING OUTCOMES

This course will provide the key conceptual tools needed to understand the most recent developments in the field of quantum computation and quantum information. Great attention will be devoted to explain quantum cryptography protocols, quantum algorithms (Deutsch, Grover, Shor) and to discuss the main physical implementation of qubits (trapped ions, superconducting qubits, quantum dots).

AIMS AND LEARNING OUTCOMES

Secure quantum key distributions for the data transfer among banks and the recent production of scientific papers sporting results obtained with quantum computer accessible in the Cloud (IBM, Rigetti) are only two of the various examples of how the relevance of quantum technologies is progressively growing in our everyday life. Starting from a critical revision of the basic concepts of quantum mechanics such as two level system (paradigm of a qubit, the fundamental building block of quantum logic) and harmonic oscillators, as well as their interaction, this course will provide the fundamentals to understand and handle concepts like quantum superposition, entanglement and quantum correlations. These ideas are at the core of the development of quantum cryptography and quantum algorithms. The advantages and limitations of state-of-the-art technologies for the concrete development of finely-controllable two level systems (trapped ions and superconducting qubits) as well as possible future game-changers will be also discussed in details.

PREREQUISITES

None

TEACHING METHODS

Blackboard lectures.

SYLLABUS/CONTENT

0. Introduction to the course  

   0.1 What are quantum technologies? 

0.2 Quantum information and quantum communication 

1. Few words about classical logic 

   1.1 Abstract representation of bits 

   1.2 Classical logical operations 

   1.3 Single-bit reversible operations 

   1.4 Shannon entropy 

   1.5 von Neumann entropy 

   1.6 Two-bit reversible operations 

2. What is a quantum bit? 

   2.1 The polarization of light

   2.2 Photon polarization

   2.3 Two level system: a paradigm for a qubit

   2.4 Basic prerequisites: Pauli matrices, time evolution of discrete level systems

3. Manipulation of qubits 

   3.1 Dynamical evolution

   3.2 Rabi oscillations

   3.3 General solution of a two level system 

4. Quantum correlations 

   4.1 No cloning-theorem

   4.2 Quantum cryptography

   4.3 Two-qubit states 

   4.4 Entanglement of two-qubit states 

   4.5 Density operator: pure and mixed states 

   4.6 Simple model of decoherence

   4.7 The Bell inequalities 

5.  Quantum algorithms  

   5.1 Quantum logic gates 

   5.2 Quantum teleportation 

   5.3 Deutsch algorithm 

   5.4 Grover search algorithm 

   5.5 Quantum error correction protocols 

   5.6 Few words on the Shor algorithm  

   (Hands-on demo of the IBM Quantum Computer)

6. Physical realization

   6.1 Di Vincenzo’s Criteria for quantum computation 

   6.2 Few words about D-Wave and quantum annealers

   6.3 Trapped ions 

   6.4 Josephson junction in the Feynman description 

   6.5 Quantum description of LC and superconducting circuits 

   6.6 Charge qubit 

   6.7 Jaynes-Cummings model: resonant and dispersive regime 

7 Quantum harmonic oscillator reloaded 

   7.1 Number states 

   7.2 Coherent states

   7.3 Squeezed states

   7.4 Wigner function

RECOMMENDED READING/BIBLIOGRAPHY

M. Le Bellac “A short Introduction to Quantum Information and Quantum Computation”. Cambridge University Press (2006).

R. P. Feynman “Lectures on Physics” vol. 3

N. K. Langford “Circuit QED-Lecture Notes”

TEACHERS AND EXAM BOARD

Exam Board

DARIO FERRARO (President)

FABIO CAVALIERE (President Substitute)

LESSONS

LESSONS START

According to the LT calendar (second semester) 

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral

ASSESSMENT METHODS

By means of questions concerning the program discussed during the lectures we will access the level of understanding and comprehension of the main subjects of the course.

Exam schedule