Quantum computing: a mathematical introduction - zajęcia fakultatywne WM-MA-S2-E2-QK

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.

Dyscyplina naukowa, do której odnoszą się efekty uczenia się

matematyka

E-Learning

E-Learning (pełny kurs) z podziałem na grupy

Grupa przedmiotów ogólnouczenianych

nie dotyczy

Opis nakładu pracy studenta w ECTS

For the lecture: class attendance 30 hours, participation in tests/exams outside of class 3 hours, consultations 2 hours, preparation for classes 5 hours, preparation for tests/exams 10 hours, All together 50 h, equivalent to 2 ECTS credits For the tutorials: 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

Poziom przedmiotu

średnio-zaawansowany

Symbol/Symbole kierunkowe efektów uczenia się

MA2_W04, MA2_W05, MA2_W06, MA2_W07, MA2_W11, MA2_W16, MA2_U10, MA2_U13, MA2_U14, MA2_U15, MA2_U19, MA2_U23, MA2_U24 MA2_K01, MA2_K02, MA2_K08

Wymagania wstępne

Linear Algebra

Koordynatorzy przedmiotu

Omid Makhmali

Efekty kształcenia

W1 – Understands the mathematical formalism of quantum computing: qubits/Bloch sphere, Hilbert spaces, Dirac bra–ket notation, unitary/Hermitian operators, projectors, the spectral theorem, and measurement. (MA2_W04, MA2_W05, MA2_W07)

W2 – Understands key QC phenomena and protocols in an information/cryptographic context: entanglement, EPR/Bell, no-cloning, teleportation, dense coding, QKD; and the idea of selected algorithms (Deutsch–Jozsa, Bernstein–Vazirani, Grover, QFT/Shor—within the covered scope). (MA2_W06, MA2_W11, MA2_W16)

U1 – Can perform calculations with quantum states and operations (including multi-qubit systems and tensor products), analyze entanglement, and use operator properties relevant to measurement. (MA2_U10, MA2_U13, MA2_U14)

U2 – Can design and analyze quantum circuits/gates (e.g., H, CNOT, bit/phase flip), including reversible implementations of classical circuits and correctness of basic constructions. (MA2_U13, MA2_U19)

U3 – Can provide mathematical justification for selected results/limitations and protocol properties (e.g., no-cloning, teleportation, Bell-type statements). (MA2_U14)

U4 – Can independently use QC literature and develop personal interests; understands the structure of analyzing quantum algorithms and computational processes. (MA2_U15, MA2_U19, MA2_U23, MA2_U24)

K1 – Is prepared to identify knowledge gaps, continue self-learning, and ask , clarifying questions that structure and validate reasoning. (MA2_K01, MA2_K02, M2_K07)

K2 – Is prepared to apply QC competence to specialization-related and socially relevant tasks (e.g., secure communication and cryptographic aspects). (MA2_K08)

Kryteria oceniania

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.

Więcej informacji

Dodatkowe informacje (np. o kalendarzu rejestracji, prowadzących zajęcia, lokalizacji i terminach zajęć) mogą być dostępne w serwisie USOSweb:

Strona przedmiotu WM-MA-S2-E2-QK w USOSweb