OVERVIEW

The course is an introduction to quantum information and computation. The theorical part is followed by an applicative one aimed to show the more recent developments of the field.

AIMS AND CONTENT

LEARNING OUTCOMES

The primary objective of the course is to learn the main concepts and phenomena underlying information technology and quantum computers - such as the principle of superposition of states, the qubit, entanglement and quantum gates - and to understand the functioning of some quantum algorithms.

AIMS AND LEARNING OUTCOMES

The aim of the course is to introduce students to computer science and quantum computing from both a theoretical and practical/applicative point of view.

At the end of the course the students will have become familiar with the most known quantum algorithms, quantum cryptography protocols, quantum information manipulation and exchange protocols. Furthermore, on a more applicative side, they will learn to write codes in the most common programming languages ​​for the quantum computers (IBM-Qiskit, Google-Cirq, Amazon-Braket).

PREREQUISITES

There are no particular prerequisites for the mathematics and physics.
The mathematical tools needed will be introduced during the course.

TEACHING METHODS

Theoretical lectures supported by more applicative ones focused on the quantum computers languages (Qiskit by IBM, CIRQ by Google, Braket by Amazon)

SYLLABUS/CONTENT

1. Physics of computation
   1. Basic concepts in Informatics: logical gates, universal and reversible logical gates
   2. Billiard ball and DNA computers
2. Mathematical tools
   1. Vector spaces and operations
   2. Tensor product
   3. Hermitian operators, eigenvectors and eigenvalues and matrix representation of an operator
3. Introduction to quantum phenomena
   1. Double slit and light polarization experiments
   2. Quantum state, quantum superposition and quantum bit (qubit)
   3. Quantum measurement
   4. Composite quantum systems and entanglement
   5. Unitary transformations, logical gates with one and two qubits
   6. Pauli operators and Bloch sphere representation
4. Introduction to quantum information
   1. Quantum parallelism, no-cloning theorem, super-dense coding and quantum teleportation
   2. Quantum algorithms: Deutch, Deutch-Joza, Bernstein-Vazirani and Simon
5. Quantum cryptography
   1. Fundamental concepts in classical cryptography: public and private key cryptography
   2. Quantum cryptography protocols: Bennett-Brassard (BB84) and Ekert91
6. Quantum algorithm for the search in a database: (Grover’s algorithm)
   1. Fundamental concepts in database search algorithms
   2. Grover’s algorithm
7. Introduction to error correcting codes
   1. Fundamental concepts in the classical case and differences with the quantum case
   2. Composite observables and their eigenvalues
   3. Quantum error correcting codes (bit-flip, small errors and phase errors)
   4. Shor’s protocol for error correcting code
8. Introduction to quantum games
   1. Introduction to game theory: classical and quantum
   2. spin-flip in star trek
   3. Prisoner dilemma: quantum and classical case
   4. Mermin’s game
9. Elitzur-Vaidman bomb tester
10. (Optional) Quantum Fourier transform and quantum phase estimation algorithm
    1. Mathematical tools and classical Fourier transform
    2. Quantum Fourier transform
    3. Quantum phase estimation algorithm
    4. Applications: quantum counting algorithm
11. (Optional) Advanced quantum algorithms
    1. Shor’s algorithm for factorizing integer numbers
    2. Harrow-Hassidim-Lloyd (HHL) algorithm
    3. Applications of HHL algorithm: linear algebra and quantum machine learning
12. (Optional) Nonlocality and entanglement in quantum mechanics
    1. Nonlocality in quantum mechanics
    2. Einstein, Podolsky, and Rosen paradox
    3. Bell’s inequality and Aspet’s experiment
    4. Greenberger–Horne–Zeilinger  nonlocal states and Zeilinger’s experiment
13. (Optional) Quantum algorithms, quantum protocol and quantum experiments implementations with the IBM quantum computers

RECOMMENDED READING/BIBLIOGRAPHY

P. Solinas – Notes: “Introduzione all’Informatica quantistica”

M. A. Nielsen e I. L. Chuang "Quantum Computation and Quantum Information", Cambridge University Press (2011)
 
N. S. Yanofsky e M. A. Mannucci  "Quantum Computing for Computer Scientists", Cambridge University Press (2008)

E. G. Rieffel and W. H. Polak "Quantum Computing: A Gentle Introduction (Scientific and Engineering Computation)"
The MIT Press (2011)

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

The lectures will start according to the academic calendar

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The examination is composed of the following components 1) a written report, 2) a written examination, and 3) optionally, an oral examination.

1. At the conclusion of the course, students will be assigned a problem to solve by developing a short piece of code for a quantum computer. Students are required to submit a written report detailing their work. Submission of this report is a prerequisite for admission to the written examination and must be completed prior to it.
2. The written examination will consist of a series of questions pertaining to topics covered during the course.
3. Students who so wish may also undertake an oral examination, which will consist of questions relating to the course material.
   In order to be eligible for the oral examination, students must first have passed the written examination.

The final grade will be based on the written report, the written examination, and, where applicable, the oral examination.

ASSESSMENT METHODS

At the end of the course, the student must be able to handle the basic concepts and techniques of quantum mechanics and quantum information.

The following items will be part of the evaluation:

- knowledge of the basic concepts in quantum information, e.g., measurement process entanglement and so on.

- knowledge of the proposed quantum algorithms and protocols