Quantum computing 1000-2M26QC
The lecture component will cover the following topics.
1. Single and multiple quantum systems
: Qubits, quantum states, Dirac notation, measurements, unitary operations, tensor products, product states, and entanglement.
2. Quantum circuits and entanglement in action:
Quantum gates, circuit model, controlled operations, Bell states, teleportation, superdense coding, and the CHSH game.
3. Quantum query algorithms and algorithmic foundations:
Query model, Deutsch–Jozsa, Bernstein–Vazirani, Simon's algorithm, reversible computation, phase kickback, and quantum Fourier transform.
4. Phase estimation, factoring, and Grover's algorithm:
Quantum phase estimation, order finding, Shor's factoring algorithm, unstructured search, and amplitude amplification.
5. Density matrices:
Mixed states, reduced states, partial trace, ensembles, and the density-matrix formulation of quantum information.
6. Quantum channels
: Quantum operations, noise, examples of channels, Kraus representations, and basic properties of quantum channels.
7. General measurements
: Projective measurements, POVMs, measurement implementation, and state discrimination.
8. Purifications and fidelity:
Purifications, fidelity, trace distance, Uhlmann-type intuition, and selected applications in quantum information.
9. Quick introduction to quantum cryptography:
Microcrypts and quantum secure one-way functions
The tutorials will reinforce the mathematical material through problem-solving sessions. The laboratory sessions will focus on implementation and simulation of basic quantum circuits and algorithms using Qiskit or similar tools. Possible lab topics include single- and multi-qubit gates, Bell states, teleportation, Deutsch–Jozsa/Bernstein–Vazirani algorithms, Grover search, quantum Fourier transform, phase estimation, and more.
Learning outcomes
Knowledge
1. Has knowledge of the basic mathematical formalism of quantum computation.
2. Knows the quantum circuit model and the role of gates, measurements, and entanglement.
3. Knows selected fundamental quantum algorithms and basic notions of quantum information.
Skills
1. Can analyze simple quantum states, measurements, circuits, and protocols.
2. Can reason about the correctness and limitations of basic quantum algorithms.
3. Can implement and simulate simple quantum circuits using Qiskit or similar tools.
Competences
1. Understands the need for mathematical rigor in quantum computation.
2. Knows the basic possibilities and limitations of quantum information processing.
3. Can assess the suitability of basic quantum algorithms for selected computational problems.
Assessment criteria
To pass the course, the student must pass the theoretical part and the practical/tutorial part. The theoretical part will be assessed by a mid-term exam and a final written exam. The practical/tutorial part will be assessed through homework, activity during tutorials, and a programming/lab test or assignment involving the implementation and simulation of simple quantum circuits using Qiskit or similar tools.
The final grade will be based on the following components:
* mid-term exam: 25%;
* final exam: 25%;
* programming/lab test or assignment: 20%;
* homework, tutorial activity, and participation: 30%.
For PhD students, an additional paper presentation and oral discussion/viva will be required. The presentation should concern an advanced topic related to quantum computing, quantum algorithms, quantum information theory, or quantum cryptography. This component may be used to increase the final grade or may be required for obtaining the highest grade.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes: