Foundations of Quantum Computation

Objectives

After successfully completing the course students should:

  • know the core concepts of quantum information and quantum computation;
  • be proficient with the standard quantum computational model;
  • understand the main quantum algorithmics techniques, and be able to use them in the design and analysis of new quantum algorithms;
  • be able to actually implement and run quantum algorithms in the software development kit Qiskit;
  • be familiar with different applications of quantum computation and its limitations. Overall these skills constitute basic knowledge for the student to further pursue the topic of Quantum Computation, either in an academic or in an industrial context.

Program

  • Linear algebra for finite-dimensional quantum mechanics
  • Inner products, norms, and orthonormal bases;
  • Dirac notation;
  • Direct sums and tensors of vector spaces.
  • Relevant classes of operators.
  • The basics of quantum information
  • The notion of a qubit and its representation in the Bloch sphere
  • Single qubit-gates.
  • Multiple qubit-systems and relevant operations.
  • Quantum measurement.
  • Quantum entanglement and some of its applications.
  • Quantum algorithmics
  • Introduction to quantum algorithms.
  • Algorithms based on phase amplification.
  • Algorithms based on the quantum Fourier transform.
  • Classical-quantum hybrid algorithms.
  • Quantum programming
  • Quantum programming in Qiskit.

Bibliography

  • M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information (10th Anniversary Edition). Cambridge University Press, 2010.
  • Hiu Yung Wong, Introduction to Quantum Computing, Springer, 2022.
  • E. Rieffel and W. Polak. Quantum Computing: A Gentle Introduction. MIT Press, 2011.
  • F. Kaye, R. Laflamme and M. Mosca. An Introduction to Quantum Computing. Oxford University Press, 2007.
  • N. S. Yanofsky and M. A. Mannucci. Quantum Computing for Computer Scientists. Cambridge University Press, 2008.
  • W. Scherer. Mathematics of Quantum Computing. Springer, 2019.
  • P. Selinger. Matrix Theory and Linear Algebra. Lyryx Learning, 2024.

Updated: