Quantum Information and Foundations Group – CSIC

Matrix Product States Lectures

Matrix product states evolution scheme

On the week of the 9th to the 13th of February, the QUINFOG group imparted a series of intensive lectures on practical and theoretical aspects of Matrix product states.

  • The different tensor network ansatz and their QIPC motivations
  • Time evolution with MPS
  • Translationally invariant ansätze
  • Ground state computation with MPS and DMRG
  • MPO and long range interactions

The lectures, intended to be practical, using C/C++ as programming language and in particular the libraries developed by J. J. García Ripoll


However, the goal was not to teach people how to use these libraries, but how to develop their own codes and read the algorithms that are already implemented. C++ is used because of convenience and license issues (CSIC does not pay for Matlab and we cannot use it in our clusters).

Below you will find the PDFs of the lectures.

  1. Foundational aspects
  2. Expected values and canonical form
  3. Linear and quadratic forms
  4. State simplification (I)
  5. State simplification (II)
  6. Time evolution basics
  7. Trotter algorithm
  8. Arnoldi method
  9. Imaginary time evolution
  10. Ground state minimization
  11. Excited states
  12. Symmetries
  13. Finite temperature