Efficient Verification of Ground States of Frustration-Free Hamiltonians

TL;DR

This paper introduces a simple, efficient method for verifying ground states of frustration-free Hamiltonians using local measurements, with sample complexity independent of system size for local gapped Hamiltonians, applicable to AKLT states.

Contribution

It presents a novel verification protocol based on local measurements with rigorous bounds, improving efficiency especially for large systems, and applies it to AKLT states on arbitrary graphs.

Findings

Sample complexity does not increase with system size for local gapped Hamiltonians.

The method requires only a constant number of samples for AKLT states on various lattices.

The approach is applicable to a broad class of many-body quantum states.

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.