Quantum Computing: a Mathematical Introduction WM-I-S2-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
(in Polish) E-Learning
(in Polish) Grupa przedmiotów ogólnouczenianych
Course coordinators
Term 2026/27_L: | Term 2025/26_L: |
(in Polish) Opis nakładu pracy studenta w ECTS
Term 2025/26_L: 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 | Term 2026/27_L: LECTURE
participation in classes: 30 hours
participation in exams outside of classes: 3 hours
participation in consultations: 4 hours
preparation for classes: 12 hrs
preparation for the exam: 26 hours
Total 75 hrs.
1.5 ECTS - direct contact with the teacher
1.5 ECTS - own work
LABORATORY
participation in classes: 30 hrs
participation in consultations: 4 hours
preparation for classes: 20 hrs
preparation for the pass: 21 hours
Total 75 hrs.
1.4 ECTS - direct contact with the teacher
1.6 ECTS - own work
|
Subject level
Learning outcome code/codes
Type of subject
Term 2025/26_L: obligatory | Term 2026/27_L: optional with unlimited choices |
Preliminary Requirements
Learning outcomes
LECTURE
Student:
W1 - knows and understands the mathematical foundations of quantum computing, in particular the concepts of a qubit, superposition and interference, Hilbert spaces, Dirac notation, unitary and Hermitian operators, projectors, spectral decomposition, and quantum measurement (I2_W10).
W2 - knows and understands the mathematical description of multi-qubit systems, tensor products and quantum entanglement, as well as the principles underlying basic quantum gates and quantum circuits (I2_W10).
W3 - knows and understands the theoretical foundations and limitations of selected quantum protocols and algorithms, in particular quantum teleportation, superdense coding, quantum key distribution, Grover's algorithm, and the quantum Fourier transform and, within the scope covered in the course, Shor's algorithm (I2_W10).
TUTORIALS/LABORATORY
Student:
U1 - is able to apply the mathematical formalism of quantum computing to determine the evolution of quantum states, calculate measurement probabilities, and analyse simple multi-qubit systems and entangled states (I2_U09).
U2 - is able to construct and analyse quantum circuits using standard quantum gates and interpret their operation in relation to the algorithm or protocol being implemented (I2_U09).
U3 - is able to analyse selected quantum algorithms and protocols and justify their properties and limitations, in particular using the linearity of quantum evolution, properties of measurement, and tensor-product structure (I2_U09).
U4 - is able to use appropriate computational tools to describe, simulate, and analyse quantum circuits and algorithms, and to interpret the resulting output (I2_U09).
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: