Quantum computing

A.Y. 2021/2022
Overall hours
Learning objectives
The course aims to provide students with a general understanding of how quantum mechanics can be applied to computational problems. Starting from classical logic concepts, the main single-qubit and two-qubit logic gates are introduced in order to analyze the main quantum algorithms. The specific purpose of the course is also to provide students with the mathematical and physical tools necessary to deal with the problems discussed throughout the course and to develop knowledge of the physical systems used to implement a quantum computer, highlighting the experimental problems associated with them.
Expected learning outcomes
At the end of the course the student must:
1. master the mathematical tools used in quantum computation;
2. know the main quantum logic gates;
3. be able to describe a quantum algorithm through a quantum circuit;
4. know the applications of the quantum Fourier transform;
5. know and formally describe the main sources of error that can occur during quantum computation;
6. apply the basic techniques of quantum error correction;
7. know the main physical systems used to implement quantum computation;
8. better understand concepts such as quantum superposition and entanglement;
9. be able to read and understand a research article on quantum computing.
Course syllabus and organization

Single session

Lesson period
First semester
Lectures will take place online through the Zoom platform. The recordings will be available on the Ariel site (https://solivarestqc.ariel.ctu.unimi.it). The course programme and teaching material will not be affected. The oral exams will be held online via Zoom and they will not be modified.
Course syllabus
· Elements of classical logic
· Elements of quantum mechanics
· Quantum mechanics as computation
· Universal computers and computational complexity
· Basic quantum algorithms and circuital representation
· Quantum Fourier transform
· Quantum factoring algorithm (Shor)
· Quantum search algorithm (Grover)
· Quantum operations and quantum maps
· Quantum error correction
· Physical implementations: two-level systems, basics of cavity QED, trapped ions, superconducting qubits
· Computation through adiabatic quantum evolution
· Recent developments of quantum computation
Prerequisites for admission
The basic knowledge of quantum mechanics is recommended.
Teaching methods
Lectures on the blackboard.
Teaching Resources
In addition to the "Lecture Notes on Quantum Computing" available on the course website (https://solivarestqc.ariel.ctu.unimi.it/), the following texts are recommended:

· M. A. Nielsen and I. L. Chuang, "Quantum Computation and Quantum Information" (Cambridge University Press).

· N. D. Mermin, "Quantum Computer Science" (Cambridge University Press).

· S. Stenholm and K.-A. Suominen, "Quantum Approach to Informatics" (Wiley-Interscience).

· S. Haroche and J.-M. Raimond, "Exploring the Quantum: Atoms, Cavities, and Photons" (Oxford Graduate Texts).

· J. A. Jones and D. Jaksch, "Quantum Information, Computation and Communication" (Cambridge University Press).

· J. Stolze and D. Suter, " Quantum Computing: A Short Course from Theory to Experiment" ( Wiley-VCH).
Assessment methods and Criteria
The exam consists of an oral exam lasting about one hour in which the student answers specific questions on quantum computing (quantum algorithms, quantum error correction, physical implementations of quantum computers,...) and proves to have acquired familiarity with the topics covered in the course.
FIS/03 - PHYSICS OF MATTER - University credits: 6
Lessons: 42 hours
Professor: Olivares Stefano
Educational website(s)
by e-mail appointment
Room A/5/C8 - 5th floor LITA building, Dipartimento di Fisica (via Celoria, 16 - 20133 Milano)