Efficient Adiabatic Preparation of Tensor Network States

Tensor network states play a fundamental role both in quantum information processing and many-body physics. In this talk, we propose and study a specific adiabatic path to prepare a family of tensor network states that are unique ground states of few-body parent Hamiltonians in finite lattices, which include normal tensor network states, as well as other relevant non-normal states. This path guarantees a gap and allows for efficient numerical simulation. In 1D we numerically investigate the preparation of a family of states with varying correlation lengths and the 1D AKLT state and show that adiabatic preparation can be much faster than standard methods based on sequential preparation. We also apply the method to the 2D AKLT state on the hexagonal lattice for which no method based on sequential preparation is known, and show that it can be prepared very efficiently for relatively large lattices. arXiv:2209.01230