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.
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.