E: minnichlab@gmail.com

P: (626)-395-3385

F: (626)-583-4963

Minnich Lab

1200 E. California Blvd, M.C. 104-44

Pasadena, CA 91125

Fall 2019

APh 250/ME 201: A numerical introduction to tensor networks for quantum simulation

 Tensor networks have emerged as a powerful tool for the numerical simulation of quantum many-body systems. This course will cover the fundamentals of tensor networks and recent algorithmic developments from a numerical perspective. Emphasis will be placed on both the theoretical foundation and practical numerical implementation of a variety of 1D and 2D tensor network algorithms. Specific topics to be covered include:

  • Fundamentals of matrix product states, canonical forms, computation of expectation values, matrix product operators, and other basics

  • Numerical renormalization group for impurity problems

  • Algorithms to find ground states, including phase estimation, variational methods, imaginary time evolution, and quantum annealing

  • Density matrix renormalization group, including time-dependent and imaginary-time algorithms, and tangent space methods

  • Pair-entangled projected states (PEPS), tensor network renormalization (TNR), 2D canonical forms, isometric PEPS, and fermionic PEPS.

Prerequisites: PH 125, CH 125 or equivalent graduate quantum mechanics course. ACM 104 or equivalent linear algebra course. 

Class notes

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