Efficient Adiabatic Preparation of Tensor Network States

TL;DR

This paper introduces an efficient adiabatic method for preparing tensor network states, including 1D and 2D AKLT states, with guarantees on gap and simulation efficiency, outperforming traditional sequential methods.

Contribution

It presents a specific adiabatic path for preparing ground states of tensor networks, enabling faster and scalable state preparation for both 1D and 2D systems.

Findings

Adiabatic preparation outperforms sequential methods in 1D.

Efficient preparation of 2D AKLT states on large lattices.

Method guarantees a finite-system gap and simulation efficiency.

Abstract

We propose and study a specific adiabatic path to prepare those 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 nonnormal states. This path guarantees a gap for finite systems and allows for efficient numerical simulation. In one dimension, we numerically investigate the preparation of a family of states with varying correlation lengths and the one-dimensional Affleck-Kennedy-Lieb-Tasaki (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 two-dimensional 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.