# Fundamentals of quantum algorithms and their implementation

**Project reference: **2212

Quantum computers are based on a completely different principle than classical computers. The aim of this project is to explain this difference. Thanks to this insight, potential students should then understand, for example, why quantum computers are able to solve the problem of exponential complexity in less than exponential time, what is the difference between quantum natural parallelism and parallel programming on HPC, or what the principle of quantum teleportation is based on.

As this field has been undergoing hectic progress in recent times, new research results are constantly being published. It is therefore not possible to cover all of these new developments in a few weeks of teaching, so this project will focus mainly on the theoretical foundations, mathematical description and practical testing of the resulting quantum circuits on real quantum computers and their simulators.

**Project Mentor:** Jiří Tomčala

**Project Co-mentor: **/

**Site Co-ordinator: **Karina Pešatová

**Learning Outcomes:
**Students should be introduced to a completely different principle of quantum computers and their programming. They should also be able to design basic quantum circuits.

**Student Prerequisites (compulsory):
**Knowledge of basic linear algebra.

**Student Prerequisites (desirable):
**Imagination and experience with Python programming.

**Training Materials:
**“Quantum Computation and Quantum Information” by Isaac Chuang and Michael Nielsen.

“Quantum Algorithm Implementations for Beginners” by various authors, which can be downloaded from here: https://arxiv.org/pdf/1804.03719.pdf

Etc.

**Workplan:
**

1st week: Quantum bits

2nd week: Single qubit operations

3rd week: Quantum gates

4th week: Quantum teleportation

5th week: Deutsch–Jozsa algorithm

6th week: Grover’s algorithm

7th week: Quantum Fourier transform

8th week: Shor’s algorithm

**Final Product Description:
**Students test their own quantum circuits on a simulator and, if possible, on a real quantum computer. This includes the correct evaluation of their measured results.

**Adapting the Project: Increasing the Difficulty:
**Attempting to create interesting modifications of the discussed algorithms.

**Adapting the Project: Decreasing the Difficulty:
**Skipping overly complicated algorithms.

**Resources:
**

**Organisation:
**IT4Innovations National Supercomputing Center at VSB – Technical University of Ostrava

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