TECNOLOGIES OF QUANTUM INFORMATION

This course introduces the foundational concepts of quantum mechanics and their application in quantum information and computation technologies. It is designed to provide students with a comprehensive understanding of quantum phenomena, leading to the development of quantum information theory and the gate model of quantum computation. By the end of the course, students will possess the knowledge required to comprehend and engage with current quantum technologies, addressing the multidisciplinary demands of diverse industrial sectors and opening new avenues for employment and specialization in the field of quantum technologies.

Upon successful completion of this course, students will be able to:

1. Understand the key concepts of quantum mechanics, including quantum states, superposition, and entanglement.
2. Apply the principles of quantum mechanics in the context of quantum information and quantum technologies.
3. Analyze and design basic quantum algorithms using the gate model of quantum computation.

Lectures, exercises and demonstrations with dedicated software. Seminars will be organized held by researchers from research institutions operating in the nanoelectronics sector.

If teaching in mixed or remote modeis required, the necessary variations may be introduced with respect to what was previously declared, in order to respect the planned program and reported in the syllabus.

To be able to take this course, students are expected to have the following foundational knowledge:

• Linear Algebra: Understanding of vector spaces, matrices, eigenvalues, and eigenvectors.
• Probability Theory: Basic concepts including probability distributions, expectation values, and statistical independence.
• Classical Mechanics.
• Electromagnetism.

Students who lack some of these prerequisites are encouraged to review the relevant materials before the course begins. Supplemental resources may be provided upon request.

1. Introduction to the Course and Quantum Technologies (lecture: 1 hour. [1,2])

2. Introduction to Quantum Mechanics for Engineers (lecture: 11 hours, exercises and lab: 10 hours. [1,2,3,4])

• Historical context and the first quantum revolution
• Review of linear algebra (with exercises)
• Postulates of quantum mechanics, quantum states, observables and measurements, time-dependent Schrödinger equation (with exercises)
• Spin and Stern-Gerlach experiment (with exercises)
• Hamiltonians and time-independent Schrödinger equation (with exercises)
• Two-level systems and Rabi oscillations (with exercises)
• Potential barriers and quantum tunneling (with exercises)
• Quantum harmonic oscillator (with exercises)

3. Quantum Information Theory (lecture: 10 hours, exercises and lab: 10 hours. [1,2,3])

• Introduction to quantum information
• Qubits and Bloch Sphere representation (with exercises)
• Entanglement and non-locality (with exercises)
• Gate model: quantum gates and circuits (with exercises)
• Quantum no-cloning theorem
• Quantum teleportation and superdense coding
• Introduction to quantum algorithms: Deutsch-Jozsa, Grover's search, and Shor’s algorithm

4. Quantum Technologies in Practice (lecture: 6 hours, exercises and lab: 10 hours. [1,2,3])

• Physical implementations of quantum computers
• Use of real quantum computers with IBM Quantum and Qiskit (with exercises)
• Superconducting quantum circuits (with exercises and simulations using Python and QuTiP)
• Current quantum technologies and future perspectives

N.B.: All theorems covered in the course may be asked during the exam.

[1] Professor's notes available on studium.

[2] Quantum Information Science. Manenti and Motta.

[3] Quantum Computation and Quantum Information. Nielsen and Chuang.

[4] C. Cohen-Tannoudji, B. Diu, and F. Lalöe. Quantum Mechanics - vol 1, volume 1. Wiley-Interscience Publication, 1977.

• The exam consists of a written test and a possible oral test. The final mark will be given by an overall evaluation of the two tests.
• Two ongoing tests are scheduled during the course.
• It is possible, at the request of the student and with the consensus of the teacher, to replace the oral with a small project. The exam will include a brief presentation of the theme, which determines the passing of the test, and the presentation of the paper, which determines the grade.
• Verification of learning can also be carried out electronically, should the conditions require it.

To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures based on educational objectives and specific needs. Students can also contact the CInAP (Centro per l’integrazione Attiva e Partecipata - Servizi per le Disabilità e/o i DSA) referring teacher within their department.

A collection of exam exercises is available in the course teaching material.

During the oral test, questions on the written test will be formulated, and questions which starting from the exposition of the topic, can range over the entire program.

The replacement paper for the oral exam consists of a deep analysis of a topic concerning the course