Efficient Adiabatic Preparation of Tensor Network States
- URL: http://arxiv.org/abs/2209.01230v3
- Date: Sun, 10 Sep 2023 01:14:49 GMT
- Title: Efficient Adiabatic Preparation of Tensor Network States
- Authors: Zhi-Yuan Wei, Daniel Malz, J. Ignacio Cirac
- Abstract summary: 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.
This path guarantees a gap for finite systems and allows for efficient numerical simulation.
- Score: 0.3683202928838613
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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