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What does a quantum computer calculate? How to read quantum circuits? What quantum algorithms work much faster than classical counterparts? What quantum algorithms are a threat to modern cryptography? All these questions, from the fundamental concepts of qubit, quantum entanglement and quantum measurements, to the details and properties of known algorithms will be studied in the course. Practical exercises will allow students to consolidate the skills of understanding and constructing quantum algorithms and circuits.

1. Classical logical circuits. Linear algebra. (Overview)

2. Qubit and single-qubit gates. Bloch Sphere.

3. Multi-qubit systems.

4. Quantum circuits. Controlled gates. Reversible computations.

5. Universal set of gates. Elementary quantum algorithms.

6. Simons problem. Grover's search algorithm.

7. Quantum Fourier transform. Phase estimation algorithm.

8. Shor's algorithms of factorization and discrete logarithm computation.

9. Quantum error correction. Elementary error correction codes.

10. Stabilizer formalism.

- M. Nielsen and I. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition, Cambridge University Press, 2010.
- E. Rieffel and W. Polak, Quantum Computing: A Gentle Introduction, The MIT Press, 2011.
- https://qiskit.org/textbook/
- https://docs.microsoft.com/en-us/azure/quantum/concepts-overview