Fondamenti e Architetture della Computazione Quantistica

Module Architettura degli Elaboratori Quantistici

The course introduces the physical description of a quantum computer and the various levels (physical, logical, control, software, and application) of the architecture. Unlike classical architectures, this architecture must be designed taking into account unique quantum properties such as superpositions, entanglement, and decoherence.

• Knowledge and Understanding – Knowledge of the main quantum hardware platforms, the main computational models, and applications to few qubits.

• Applying Knowledge and Understanding – Ability to apply basic theoretical techniques and approximations for the analysis and simulation of quantum computers.

• Communication Skills – Communication skills in the field of quantum computing.

• Learning Skills – Acquisition of knowledge tools for continuous updating of knowledge in the field, through access to computer labs, online facilities, and specialized literature

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Teaching Method

Lessons will be delivered in person. The theoretical content will be presented by the instructor using slides and a whiteboard. Active student participation will be encouraged through questions and discussions in the classroom.

If the course is taught in a blended or distance learning format, any necessary changes to the previously stated curriculum may be made in order to comply with the planned program outlined in the syllabus.

To attend this course, students must have the following basic knowledge:

• Linear Algebra: Understanding vector spaces, matrices, eigenvalues, and eigenvectors

• Probability Theory: Basic concepts, including probability distributions, expected values, and statistical independence

• Classical Mechanics and Electromagnetism

• Elements of Quantum Physics

Students who do not have any of these prerequisites are encouraged to review the relevant material before starting the course.

Class Attendance

For a thorough understanding of the topics covered and the methodologies presented, regular class attendance is strongly recommended.

Quantum Computer Architecture

Bits and Qubits – States and Logic Gates of a Classical Computer, Logical Reversibility. States of a Quantum Computer. Quantum Logic Gates and Reversibility. The Quantum Circuit Model. Measurement: Born Rule and Holevo Limit. Generation of Arbitrary States of One or Two Qubits.

General Characteristics and Simple Examples – Computing in General. The Deutsch Problem. The Bernstein-Vazirani Problem. The Simon Problem. Construction of Toffoli Logic Gates

Quantum Hardware – Photon Polarization. Electronic and Nuclear Spin. Two-Level Atoms. Artificial Superconducting and Semiconducting Atoms.

Decoherence and Quantum Error Correction – Decoherence. Classical Phase Randomization. A Simple Example of Quantum Error Correction. The Physics of Error Generation. Error Diagnostics (Syndrome). 5- and 7-Qubit Protocols.

Few-Qubit Protocols – Bell States. Quantum cryptography. Bit commitment. Dense coding. Teleportation. The GHz problem.

[2] Giuliano Benenti, Giulio Casati, Simone Montangero, Il computer impossibile, Raffaello Cortina Editore, 2025

[3] Giuseppe A. Falci, lecture notes and slides

Assessment Methods

The oral exam includes: (a) presentation of a topic agreed upon in advance with the instructor; (b) presentation of a topic chosen by the candidate during the exam from three topics (of varying difficulty) proposed by the instructor. Passing the exam depends exclusively on test (a), while test (b) contributes to the final grade.

The evaluation is based on: relevance of answers to the questions asked; level of understanding of the content presented; accuracy in presenting calculations; ability to connect with other topics in the course (or previous courses) and to provide examples; and command of language and clarity of presentation.

These tests may be conducted online, if circumstances require.

The exam is designed to thoroughly assess the student's preparation, analytical and reasoning skills on the topics covered during the course, as well as the appropriateness of the technical language used.

The following criteria will generally be used to assign the final grade:

- Not approved: The student demonstrates minimal mastery of the agreed-upon topic or shows serious deficiencies in basic concepts during the exam.

- 18-23: The student demonstrates minimal mastery of basic concepts, and their presentation and connection skills are modest.

- 24-27: The student demonstrates good mastery of the course content, and their presentation and connection skills are good, and they solve the exercises with few errors.

- 28-30 with honors: The student has mastered all the course content and is able to present it thoroughly and connect it critically; they solve the exercises completely and without errors.

Students with disabilities and/or learning disabilities (LD) must contact the instructor, the CInAP representative of the DMI (Prof. Daniele), and CInAP well in advance of the exam to communicate their intention to take the exam with appropriate compensatory measures.

The exam is designed to thoroughly assess the student's preparation, analytical and reasoning skills on the topics covered during the course, as well as the appropriateness of the technical language used.

Sample Questions

- Describe the quantum measurement process and its implications for quantum computing.

- Describe a physical implementation of quantum hardware.

- Define entanglement and illustrate one of its applications.

- Derive the coherence decay of a qubit subjected to classical Gaussian noise.

Please note that these questions are purely indicative: the actual questions asked during the exam may differ, even significantly, from those listed here.

The exam is intended to thoroughly assess the student's preparation, analytical and reasoning skills on the topics covered during the course, as well as the appropriateness of the technical language used.