Efficient Verification of Ground States of Frustration-Free Hamiltonians
- URL: http://arxiv.org/abs/2206.15292v3
- Date: Thu, 4 Jan 2024 09:37:45 GMT
- Title: Efficient Verification of Ground States of Frustration-Free Hamiltonians
- Authors: Huangjun Zhu, Yunting Li, and Tianyi Chen
- Abstract summary: We propose a recipe for verifying the ground states of general frustration-free Hamiltonians based on local measurements.
We derive rigorous bounds on the sample complexity by virtue of the quantum detectability lemma and quantum union bound.
Our work is of interest not only to many tasks in quantum information processing, but also to the study of many-body physics.
- Score: 28.03059224016627
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Ground states of local Hamiltonians are of key interest in many-body physics
and also in quantum information processing. Efficient verification of these
states are crucial to many applications, but very challenging. Here we propose
a simple, but powerful recipe for verifying the ground states of general
frustration-free Hamiltonians based on local measurements. Moreover, we derive
rigorous bounds on the sample complexity by virtue of the quantum detectability
lemma (with improvement) and quantum union bound. Notably, the number of
samples required does not increase with the system size when the underlying
Hamiltonian is local and gapped, which is the case of most interest. As an
application, we propose a general approach for verifying
Affleck-Kennedy-Lieb-Tasaki (AKLT) states on arbitrary graphs based on local
spin measurements, which requires only a constant number of samples for AKLT
states defined on various lattices. Our work is of interest not only to many
tasks in quantum information processing, but also to the study of many-body
physics.
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