9600-0016/01 – Introduction to Quantum Computing (IQC)
| Gurantor department | IT4Innovations | Credits | 4 |
| Subject guarantor | prof. RNDr. Marek Lampart, Ph.D. | Subject version guarantor | prof. RNDr. Marek Lampart, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2021/2022 | Year of cancellation | |
| Intended for the faculties | FEI, FBI, USP, FS, EKF, HGF, FMT, FAST | Intended for study types | Follow-up Master, Master |
Subject aims expressed by acquired skills and competences
The aim of the course is to master the elementary concepts of quantum computing without requiring knowledge of quantum physics and to acquire basic skills related to register-based programming. Students will learn to analyze and implement simple quantum algorithms, understand the differences between classical and quantum computational models, and be able to use quantum simulators as well as access real quantum computers.
Teaching methods
Lectures
Tutorials
Project work
Summary
This course is an introductory class in quantum computing, focusing on the fundamental elements of quantum computational theory without assuming prior knowledge of quantum physics. The introduction to quantum theory from the perspective of computer science begins with an explanation of the essential concepts, aiming to demonstrate several elementary examples of quantum speedup as well as core applications: Shor’s factorization algorithm, Grover’s search algorithm, and quantum error correction. Theoretical knowledge is then demonstrated in practice on a quantum computer (simulator), such as IBM Qiskit or NVIDIA CUDA-Q.
The course is intended for 1st- and 2nd-year Master’s students at VSB-TUO. Knowledge of linear algebra is a prerequisite.
Compulsory literature:
Recommended literature:
1. BENENTI, G.; CASATI, G.; ROSSINI, D.; STRINI, G. Principles of Quantum Computation and Information - A Comprehensive Textbook. World Scientific, 2018.
2. STRUBELL, E. An Introduction to Quantum Algorithms. COS498 - Chawathe, 2011.
3. ABHIJITH, J. et al. Quantum Algorithm Implementations for Beginners. Los Alamos National Laboratory USA, 2018.
Additional study materials
Way of continuous check of knowledge in the course of semester
Credit:
1. Test on the basics of quantum computational theory – max. 10 points
2. Test on classical quantum algorithms – max. 10 points
3. Individual assignment on the implementation of a quantum algorithm – max. 20 points
Final Exam:
-written test or oral examination
E-learning
Other requirements
No other requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
1. Basic properties of a qubit, Bloch sphere: classical bit vs. quantum bit, qubit state, superposition, geometric representation on the Bloch sphere; examples of simple states (|0⟩, |1⟩, |+⟩).
2. Qubits and their states, Dirac notation: fundamental principles of linear algebra in quantum informatics, Dirac notation, tensor products; description of multi-qubit states, separability and quantum entanglement.
3. Reversible operations on a qubit, qubit measurement: unitary operations, Pauli matrices, Hadamard gate; measurement in the computational basis, wave function collapse, probabilistic nature of outcomes.
4. Quantum entanglement: formal definition, Bell pair states; significance of quantum entanglement for quantum algorithms and communication.
5. Deutsch–Jozsa and Bernstein–Vazirani algorithms: first demonstrative algorithms of quantum speedup; difference between classical and quantum solutions, their complexity.
6. Simon’s algorithm: problem description, solution using quantum circuits; historical significance for the development of Shor’s algorithm.
7. Grover’s algorithm: principle of quantum search; diffuser, oracle, quadratic speedup compared to classical search.
8. Quantum Fourier Transform and Shor’s algorithm: mathematical foundation of QFT, efficient implementation; Shor’s algorithm for factorization and its significance for cryptography.
9. RSA and decoding: classical cryptography, principle of RSA; application of quantum factoring to breaking RSA.
10. Introduction to quantum error correction: noise and decoherence in quantum computers; example of a simple repetition code.
11. Error diagnosis and correcting codes: syndrome measurements, principle of stabilizer codes; examples of error models and their correction.
12. Quantum cryptography and applications: BB84 protocol, quantum key distribution; simple examples of practical use of quantum communication.
Exercises:
1. Installation and first steps: installation of Qiskit and access to IBM Quantum Platform; building the first simple circuit and running it on a simulator.
2.–3. Tensor algebra and interpretation of qubits: working with simple two-qubit states; creating entangled states, visualization of results.
4. Reversible operations and measurement: implementation of Pauli gates and the Hadamard gate; measurement simulation, probabilistic distribution of outcomes.
5. Quantum entanglement in practice: generation of Bell pairs, verification of entanglement; experiments with multi-qubit states.
6. Deutsch–Jozsa algorithm: implementation of an oracle, comparison with the classical solution.
7. Bernstein–Vazirani algorithm: implementation and testing with different bit lengths.
8. Simon’s algorithm: building the oracle, finding the period using a quantum circuit.
9. Grover’s algorithm: implementation of an oracle, diffuser, and search in a small database; comparison with classical search.
10. Quantum Fourier Transform: implementation of QFT in Qiskit; analysis of complexity and outputs.
11. Shor’s algorithm: simulation of factorization of small numbers; limits of current quantum hardware.
12. Error correction and cryptography: implementation of a simple repetition code; demonstration of the BB84 protocol on a simulator.
Projects:
Individual assignment: implementation of a quantum algorithm (e.g., Grover’s, Shor’s, Simon’s, or a quantum cryptography protocol) on a selected quantum simulator or a real quantum computer (IBM Qiskit, NVIDIA CUDA-Q). The deliverables are the code, a report, and a presentation of the results.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction