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.