01GZZUU

A.A. 2023/24

Course Language

Inglese

Degree programme(s)

Master of science-level of the Bologna process in Quantum Engineering - Torino

Course structure

Teaching | Hours |
---|---|

Lezioni | 40 |

Esercitazioni in aula | 20 |

Lecturers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
---|---|---|---|---|---|---|---|

Adami Riccardo | Professore Ordinario | MAT/05 | 40 | 20 | 0 | 0 | 1 |

Co-lectuers

Context

SSD | CFU | Activities | Area context |
---|---|---|---|

MAT/05 MAT/05 |
3 3 |
D - A scelta dello studente C - Affini o integrative |
A scelta dello studente Attività formative affini o integrative |

2023/24

The course gives a presentation of Quantum Mechanics together with the necessary mathematical tools, from finite dimensional linear algebra to Fock Spaces. Example and applications are numerous and developed, aiming at applications on quantum computing, cryptography, teleportation, information.

The course gives a presentation of Quantum Mechanics together with the necessary mathematical tools, from finite dimensional linear algebra to Fock Spaces. Example and applications are numerous and developed, aiming at applications on quantum computing, cryptography, teleportation, information.

Knowledge: basics of quantum mechanics mastering the mathematical formalism at a rigorous level; interpretation of quantum mechanics and related contemporary debate; applications to devices, from transistors to contemprary sigle-particle technology.
Skills: solving problems on spectra of quantum observables, probability transitions, from spin systems to atomic systems. Write down quantum mechanical models for simple systems and discuss them. Reading autonomously classics of quantum mechanics as well as modern treatises.

Knowledge: basics of quantum mechanics mastering the mathematical formalism at a rigorous level; interpretation of quantum mechanics and related contemporary debate; applications to devices, from transistors to contemprary sigle-particle technology.
Skills: solving problems on spectra of quantum observables, probability transitions, from spin systems to atomic systems. Write down quantum mechanical models for simple systems and discuss them. Reading autonomously classics of quantum mechanics as well as modern treatises.

Linear algebra, matrices, unitary and hermitian transformations. Diagonalization, quadratic forms, spectral theorem for finite-dimensional spaces.

Linear algebra, matrices, unitary and hermitian transformations. Diagonalization, quadratic forms, spectral theorem for finite-dimensional spaces.

Two-slit experiment. Superposition principle. Two state systems: polaroid, spin, qubit. The problem of measurement. Structure of finite-dimensional Hilbert spaces. Self-adjointness and observable. Spectrum. Spectral theory, simultaneous diagonalization and compatible observable. Collapse. Statistical mixtures, density matrix. Bell inequalities, locality, EPR, interpretation. Examples: quantum algorithms (Grover), quantum teleportation, quantum cryptography.
Ininite-dimensional Hilbert spaces. Potential well, Dirac potential, Harmonic oscillator, Hydrogen atom.
Creation and annihilation of particle: Fock spaces. Some examples from quantum electrodynamics.

Two-slit experiment. Superposition principle. Two state systems: polaroid, spin, qubit. The problem of measurement. Structure of finite-dimensional Hilbert spaces. Self-adjointness and observable. Spectrum. Spectral theory, simultaneous diagonalization and compatible observable. Collapse. Statistical mixtures, density matrix. Bell inequalities, locality, EPR, interpretation. Examples: quantum algorithms (Grover), quantum teleportation, quantum cryptography.
Ininite-dimensional Hilbert spaces. Potential well, Dirac potential, Harmonic oscillator, Hydrogen atom.
Creation and annihilation of particle: Fock spaces. Some examples from quantum electrodynamics.

Blackboard lectures and slides, with exercises. Participation and interaction is strongly encouraged.

Blackboard lectures and slides, with exercises. Participation and interaction is strongly encouraged.

Luigi E. Picasso, “Lectures in Quantum Mechanics”, Springer 2015
Luigi E. Picasso, E. d’Emilio, “Problems in Quantum Mechanics with Solutions”, Springer 2015.
Griffiths, Schoeter, “Introduction to Quantum Mechanics”, 1995
Preskill, Lecture Notes on Quantum Information and Computation, online.

Luigi E. Picasso, “Lectures in Quantum Mechanics”, Springer 2015
Luigi E. Picasso, E. d’Emilio, “Problems in Quantum Mechanics with Solutions”, Springer 2015.
Griffiths, Schoeter, “Introduction to Quantum Mechanics”, 1995
Preskill, Lecture Notes on Quantum Information and Computation, online.

...
Written exercises on the programme of the course, with a possible oral integration

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

Written exercises on the programme of the course, with a possible oral integration

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

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Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY