IA066 Introduction to Quantum Computing

Fakulta informatiky
podzim 2023
Rozsah
2/0/0. 2 kr. (plus ukončení). Ukončení: zk.
Vyučující
RNDr. Vít Musil, Ph.D. (přednášející)
prof. RNDr. Antonín Kučera, Ph.D. (cvičící)
Garance
prof. RNDr. Antonín Kučera, Ph.D.
Katedra teorie programování – Fakulta informatiky
Dodavatelské pracoviště: Katedra teorie programování – Fakulta informatiky
Rozvrh
Po 12:00–13:50 C525
Předpoklady
Linear algebra in a complex field; No knowledge of quantum physics is assumed.
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
předmět má 63 mateřských oborů, zobrazit
Cíle předmětu
The course introduces students to the core principles of quantum mechanics as applied to computing. Initially, we confront our classical expectations with quantum surprises through experiments to discover fundamental phenomena such as superposition, interference and measurement. We then establish a mathematical framework to underpin these concepts. Students will learn about basic concepts and methods used in quantum computing as well as famous key algorithms that offer advantages over classical computing. The course aims to provide theoretical knowledge and skills, preparing students for advanced studies or careers in quantum technologies. In contrast to popularization lectures, the focus is on understanding the mathematical rigour.
Výstupy z učení
After completing the course, students will be able to understand:
- the mathematical foundations of quantum computing
- basic principles of quantum algorithm design
- basic quantum circuit design
- basic elements of quantum cryptography
- Grover's search and Shor's period-finding algorithms
Osnova
  • Introduction: What is quantum computing, and why look at it.
  • Classical expectations & quantum surprises: Demonstration of experiments with spinning neutrons in a magnetic field; Building a formal model, discussion of measurement, unavoidable complexity.
  • Superposition: Introducing 'signed' probabilities; Constructive and destructive interference.
  • Postulates of quantum mechanics: State space; Qbit and its measurement (Born rule); The evolution of a quantum system.
  • Operations on a Qbit: Properties of unitary transforms; Quantum gates and circuits; I, H, X, Z gates.
  • Protocols using on Qbit: Quantum key distribution (BB84); Bit commitment.
  • Composite systems: Tensor product and entanglement; Measurement revisited, Generalized Born rule.
  • Operations on Qbits: Unitary transforms, Product and entanglement gates, CNOT; Postulates revisited; No cloning theorem;
  • Dense coding & Teleportation: Bell basis and duality;
  • Reversible computation of a Boolean function: Unitary implementation of any function; Quantum parallelism; Phase query;
  • Protocols using a few Qbits: Deutsch's problem'; Bernstein-Vazirani problem; Simon's problem.
  • Grover's Search algorithm
  • Shor's factoring algorithm: Discrete Fourier transform; Period finding.
Literatura
  • GRUSKA, Jozef. Quantum computing. London: McGraw-Hill Companies, 1999, xv, 439. ISBN 0077095030. info
Výukové metody
Lectures and tutorials
Metody hodnocení
Written test, oral exam.
Vyučovací jazyk
Angličtina
Další komentáře
Studijní materiály
Předmět je vyučován každoročně.
Předmět je zařazen také v obdobích podzim 2002, podzim 2003, podzim 2004, podzim 2005, podzim 2006, podzim 2007, podzim 2008, podzim 2009, podzim 2010, podzim 2011, podzim 2012, podzim 2013, podzim 2014, podzim 2015, podzim 2016, podzim 2017, podzim 2018, podzim 2019, podzim 2020, podzim 2021, podzim 2022, podzim 2024.