Building an adiabatic quantum computer simulation in the classroom

We present a didactic introduction to adiabatic quantum computation (AQC) via the explicit construction of a classical simulator of quantum computers. This constitutes a suitable route to introduce several important concepts for advanced undergraduates in physics: quantum many-body systems, quantum phase transitions, disordered systems, spin-glasses, and computational complexity theory. (C) 2018 American Association of Physics Teachers.The authors want to acknowledge the faculty and students of the Facultad de Informática of UCM (Madrid) for their kind invitation to deliver this crash course, particularly to I. Rodríguez-Laguna and N. Martí. The authors would also like to thank G. Sierra for very useful comments on the manuscript. This work was funded by the Spanish government through Grant Nos. FIS2015-69167-C2-1-P and FIS2015-66020-C2-1-