# ELEMENTS OF QUANTUM COMPUTING

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iten
Code
98389
2021/2022
CREDITS
6 credits during the 3nd year of 8759 Computer Science (L-31) GENOVA

6 credits during the 2nd year of 9011 Mathematics (LM-40) GENOVA

SCIENTIFIC DISCIPLINARY SECTOR
FIS/02
LANGUAGE
Italian
TEACHING LOCATION
GENOVA (Computer Science)
semester
1° Semester
Teaching materials

OVERVIEW

The course is an introduction to quantum information and computation.

## AIMS AND CONTENT

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 and CIRQ by Google)

SYLLABUS/CONTENT

1.    Physics of computation
1.1 Basic concepts in Informatics: logical gates, universal and reversible logical gates
1.2 Billiard ball and DNA computers
2   Mathematical tools
2.1 Complex numbers, vector space and operations
2.2 Tensor product
2.3 Hermitian operators, eigenvectors and eigenvalues and matrix representation of an operator
3    Introduction to quantum phenomena
3.1 Double slit and light polarization experiments
3.2 Quantum state, quantum superposition and quantum bit (qubit)
3.3 Quantum measurement
3.4 Composite quantum systems and entanglement
3.5 Unitary transformations, logical gates with one and two qubits
3.6 Pauli operators and Bloch sphere representation
4    Introduction to quantum information
4.1 Quantum parallelism, no-cloning theorem, super-dense coding and quantum teleportation
4.2 Quantum algorithm: Deutch, Deutch-Joza, Bernstein-Vazirani and Simon
5    Quantum cryptography
5.1 Fundamental concepts in classical cryptography: public and private key cryptography
5.2 Quantum cryptography protocols: BB84 and Ekert91
6    Quantum algorithm for the search in a database: (Grover’s algorithm)
6.1 Fundamental concepts in database search algorithms
6.2 Grover’s algorithm
7    Quantum Fourier transform and quantum phase estimation algorithm
7.1 Mathematical tools
7.2 Quantum Fourier transform and quantum phase estimation algorithm
7.3 Applications: quantum counting algorithm
8 HHL algorithm (for linear algebra) and Shor’s algorithm (for integer factorization)
9   Introduction to error correcting codes
9.1 Fundamental concepts in the classical case and differences with the quantum case
9.2 Composite observables and their eigenvalues
9.3 Quantum error correcting codes
10 Algorithm and quantum protocols implementation with the IBM quantum experience

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

Ricevimento: Meeting with the students are taken by appointments. Contact: Paolo Solinas, Dipartimento di Fisica, via Dodecaneso 33, 16146 Genova piano 8, studio S819 telefono: 010 3536260 email: solinas@fisica.unige.it

Exam Board

PAOLO SOLINAS (President)

PIERANTONIO ZANGHI'

ALESSANDRO VERRI (Substitute)

## LESSONS

Teaching methods

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

LESSONS START

The lectures will start according to the academic calendar

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

## EXAMS

Exam description

The exam is composed by an oral examination and a home assignment.
In home assignment the student will be asked to solve a simple problem by writing a code for a quantum computer and he/she will be asked to write a short report.