OVERVIEW

The purpose of this course is to illustrate the physical principles underlying quantum computation and quantum information theory.

The role played by quantum properties such as the superposition and entanglement in quantum algorithms and communication protocols will be discussed in detail.

Additionally, two of the main experimental platforms (trapped ions and superconducting circuits) on which these quantum technologies are currently implemented will be described.

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

At the end of this course, the student will be able to:

i) describe and characterize quantum phenomena such as the superposition and entanglement;

ii) understand the role played by these phenomena in quantum computation algorithms and communication protocols;

iii) analyze the operations of devices based on atomic physics (trapped ions) and solid-state physics (superconducting circuits) in view of their applications as qubits.

PREREQUISITES

None

TEACHING METHODS

Lectures will be delivered using a blackboard.

SYLLABUS/CONTENT

0. Introduction to the course  

   0.1 What are quantum technologies?

   0.2 Quantum information and quantum communication 

   0.3 Platforms for quantum computing.

1. Two-level quantum system 

   1.1 Physical examples

   1.2 General solution of the dynamics

   1.3 Rabi oscillations

   1.4 Bloch sphere

2 Quantum harmonic oscillator 

   2.1 Number states 

   2.2 Coherent states

3 Time evolution 

   3.1 General considerations

   3.2 Instantaneous evolution 

   3.3 Adiabatic theorem

   3.4 Quantum speed limit 

4. Quantum correlations 

   4.1 Two-qubit states

   4.2 Entanglement of two-qubit states 

   4.3 Density operator: pure and mixed states 

   4.4 Measurement of the entanglement

   4.5 Simple model of decoherence

   4.6 The Bell inequalities 

5.  Quantum algorithms  

   5.1 No go theorems

   5.2 Quantum cryptography

   5.3 Few words on classical logic

   5.4 Quantum logic gates

   5.5 Quantum teleportation 

   5.6 Deutsch algorithm 

   5.7 Grover search algorithm 

   5.8 Quantum error correction protocols 

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 Few words about superconductivity

   6.5 Josephson junction in the Feynman description

   6.6  Quantization of an LC circuit

   6.7  Description of a superconducting circuits 

   6.8 Charge qubit and transmon qubit

   6.9 Few words about circuit QED

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)

NICCOLO' TRAVERSO ZIANI

FABIO CAVALIERE (President Substitute)

LESSONS

LESSONS START

Accroding to the official calendar of the Physics Department (Third Year)

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral exam held on the blackboard.  

ASSESSMENT METHODS

Learning is assessed through an oral exam consisting of the discussion of two topics covered in the lectures:

one chosen by the student (approximately 20 minutes of presentation at the blackboard) and one chosen by the examination committee.

The assessment will be conducted in accordance with the regulations and guidelines concerning disabilities and specific learning disorders (SLD)

Exam schedule

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.