Quantum computing: a mathematical introduction WM-I-S2-E4-QC

Quantum technologies are opening a new direction in computation by exploiting principles that have no counterpart in classical information processing. Quantum computers encode and manipulate information in ways that can, for specific tasks, outperform standard machines by a dramatic margin. One widely discussed example comes from cryptography: several commonly used security schemes depend on the practical difficulty of factoring very large integers, whereas quantum methods (notably Shor’s algorithm) indicate that such problems can be handled efficiently under an appropriate quantum model.

Ongoing advances in hardware and theory, together with substantial investment from both industry and public institutions, have made quantum computing an increasingly active area of research and development. The aim of this course is to provide a mathematically grounded introduction to the subject, developing the core concepts and techniques needed to read further material and pursue more advanced study.

A background in quantum mechanics or programming is useful but not assumed and is not necessary. Students are expected to be comfortable with trigonometry, complex numbers, and linear algebra, and to be willing to work carefully with formal mathematical reasoning. Curiosity and persistence will be essential throughout the course. All necessary background will be reviewed during the course.

The format of the lectures and tutorials will be in a classroom with a blackboard and there will not be any mandatory programming involved.

(in Polish) Dyscyplina naukowa, do której odnoszą się efekty uczenia się

information and communication technology

(in Polish) E-Learning

(in Polish) E-Learning (pełny kurs) z podziałem na grupy

(in Polish) Grupa przedmiotów ogólnouczenianych

(in Polish) nie dotyczy

(in Polish) Opis nakładu pracy studenta w ECTS

For the lecture: participation in tests/exams outside of class 3 hours, consultations 6 hours, preparation for classes 12 hours, preparation for tests/exams 24 hours, All together 75 h, equivalent to 3 ECTS credits For the laboratory: class attendance 30 hours, consultations 5 hours, preparation for classes 20 hours, preparation for tests/exams 20 hours, All together 75 h, equivalent to 3 ECTS credits

Subject level

intermediate

Learning outcome code/codes

I2_W01, I2_W03, I2_W10, I2_W11, I2_W02 I2_U01, I2_U02, I2_U06, I2_U07, I2_U09, I2_U08, I2_U12 I2_K01, I2_K02, I2_K06

Type of subject

obligatory

Preliminary Requirements

Linear Algebra

Course coordinators

Omid Makhmali

Learning outcomes

W1 - Understands the core mathematical and conceptual foundations of QC: superposition/interference, qubits and the Bloch sphere, Hilbert spaces and bra-ket notation, unitary/Hermitian operators, projectors, the spectral theorem, and measurement. (I2_W01, I2_W03)

W2 - Understands QC as a specialized CS domain and its limits/applications: multi‑qubit systems and tensor products, entanglement, gates/circuits and reversible classical implementations, and selected protocols/algorithms (dense coding, QKD, teleportation, Grover, QFT/Shor-within covered scope). (I2_W02, I2_W10, I2_W11)

U1 - Can model and analyze quantum computational processes mathematically: compute state evolution and measurement statistics; work with tensor products and identify entanglement in standard examples. (I2_U01, I2_U02)

U2 - Can design and analyze quantum circuits: use standard gates (H, CNOT, bit/phase flip), reason about correctness/cost at the level covered, and relate reversible classical circuits to quantum implementations. (I2_U02, I2_U06)

U3 - Can give formal justification for key limitations and protocol properties (e.g., no‑cloning, teleportation structure, Bell‑type reasoning as presented in class). (I2_U02, I2_U06)

U4 - Can communicate QC results clearly in written/oral form (circuits, short technical notes/presentations) and use advanced tools/methods for the domain when needed (e.g., circuit description/simulation in labs). (I2_U07, I2_U09)

U5 - Can plan further self‑study and use specialist literature (incl. English if required) to extend understanding beyond the course topics. (I2_U08,I2_U12)

K1 - Is prepared to identify gaps in knowledge and engage in continuous self‑learning. (I2_K01)

K2 - Is prepared to work systematically in longer‑term tasks/projects (e.g., lab assignments/mini‑project), including collaboration where applicable. (I2_K02)

K3 - Is prepared to apply QC competence to specialization-related and socially relevant tasks (e.g., secure communication and cryptographic aspects). (I2_K06)

Assessment criteria

For all learning outcomes, the following assessment criteria are adopted for all forms of verification:

grade 5: fully achieved (no obvious shortcomings),

grade 4.5: achieved almost fully and criteria for awarding a higher grade are not met,

grade 4: largely achieved and the criteria for a higher grade are not met,

grade 3.5: largely achieved - with a clear majority of positives - and the criteria for granting a higher grade are not met,

grade 3: achieved for most of the cases covered by the verification and criteria for a higher grade are not met,

grade 2: not achieved for most of the cases covered by the verification.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of WM-I-S2-E4-QC in USOSweb