Quantum Computation 1

Course guarantor:

Lecturer:

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Supervisor:

Department of Applied Mathematics

Synopsis:

The course introduces the student to basic principles of quantum computation and shows the difference between classical and quantum mechanics. Quantum computation uses quantum circuits, which will be demonstrated in the Qiskit SDK. The course will gradually introduce the student to such concepts the state of a quantum system and its visualization, measurements, basic gates and their composition, and the so-called entanglement. The student will be introduced to the BB84 and E91 protocols as demonstrations of the properties of quantum states. The course will also cover quantum teleportation, quantum oracle queries, the Deutsch-Jozsa algorithm, the quantum Fourier transform, the phase estimation algorithm, and the Shor algorithm.

Requirements:

Syllabus of lectures:

1. Motivation for quantum technologies, differences between classical and quantum mechanics, introduction to the Qiskit environment.

2. State of a quantum system, probabilistic and quantum bits, superposition, measurement and collapse of the wave function.

3. State of a quantum system, visualization of qubit - Bloch sphere, unitarity of time evolution.

4. Single qubit gates as rotations, measurement in arbitrary basis, BB84 protocol for quantum key distribution.

5. Two qubit quantum register, measurement and partial measurement, entanglement, Bell (EPR) states, E91 protocol.

6. Two-qubit gates and their compositions, impossibility of qubit cloning.

7. Superdense coding, multi-qubit quantum registers, multi-qubit gates, quantum teleportation, no-signalling principle.

8. Classical and quantum circuits, arithmetic on classical and quantum computer (addition), universal quantum computer, universal set of gates.

9. Oracle querying, simple quantum algorithms (Deutsch-Jozs).

10. Quantum Fourier transform and its implementation.

11. Quantum arithmetic using quantum Fourier transform, quantum algorithm for phase estimation.

12. Shor's algorithm I.

13. Shor's algorithm II.

Syllabus of tutorials:

1. Motivation for quantum technologies, differences between classical and quantum mechanics, introduction to the Qiskit environment.

2. State of a quantum system, probabilistic and quantum bits, superposition, measurement and collapse of the wave function.

3. State of a quantum system, visualization of qubit - Bloch sphere, unitarity of time evolution.

4. Single qubit gates as rotations, measurement in arbitrary basis, BB84 protocol for quantum key distribution.

5. Two qubit quantum register, measurement and partial measurement, entanglement, Bell (EPR) states, E91 protocol.

6. Two-qubit gates and their compositions, impossibility of qubit cloning.

7. Superdense coding, multi-qubit quantum registers, multi-qubit gates, quantum teleportation, no-signalling principle.

8. Classical and quantum circuits, arithmetic on classical and quantum computer (addition), universal quantum computer, universal set of gates.

9. Oracle querying, simple quantum algorithms (Deutsch-Jozs).

10. Quantum Fourier transform and its implementation.

11. Quantum arithmetic using quantum Fourier transform, quantum algorithm for phase estimation.

12. Shor's algorithm I.

13. Shor's algorithm II.

Study Objective:

The course introduces the student to basic principles of quantum computation and shows the difference between classical and quantum mechanics. Quantum computation uses quantum circuits, which will be demonstrated in the Qiskit SDK. The course will gradually introduce the student to such concepts the state of a quantum system and its visualization, measurements, basic gates and their composition, and the so-called entanglement. The student will be introduced to the BB84 and E91 protocols as demonstrations of the properties of quantum states. The course will also cover quantum teleportation, quantum oracle queries, the Deutsch-Jozsa algorithm, the quantum Fourier transform, the phase estimation algorithm, and the Shor algorithm.

Study materials:

1. Lipton, R. J., Regan, K. W.: Introduction to Quantum Algorithms via Linear Algebra, 2nd Edition

MIT press 2021

ISBN 9780262045254

2. Wong, G. T.: Introduction to Classical and Quantum Computing

Rooted Grove 2022

ISBN 979-8985593105

3. Johnston, E., Harrigan, N., Gimeno-Segovia, M.: Programming Quantum Computers: Essential Algorithms and Code Sample

O'Reilly Media 2019

ISBN 4920396813

4. Norlen, H.: Quantum Computing in Practice with Qiskit and IBM Quantum Experience

Packt Publishing 2020

ISBN 1838828443

Note:

This course is presented in English.

Further information:

https://courses.fit.cvut.cz/QNIE-QC1

No time-table has been prepared for this course

The course is a part of the following study plans: