A Hidden Quantum Markov model framework for Entanglement and Topological Order in the AKLT Chain

TL;DR

This paper develops a hidden quantum Markov model framework to analyze entanglement and topological order in the AKLT chain, linking quantum machine learning with many-body physics.

Contribution

It introduces a novel HQMM framework for the AKLT state, capturing entanglement and SPT order through quantum emission and observation channels.

Findings

Maximal entanglement captured by quantum channels.

SPT order induces covariance in decoding channels.

Establishes a connection between quantum ML and topological phases.

Abstract

This paper introduces a hidden quantum Markov models (HQMMs) framework to the Affleck-Kennedy-Lieb-Tasaki (AKLT) state-a cornerstone example of a symmetry-protected topological (SPT) phase. The model's observation system is the physical spin-1 chain, which emerges from a hidden spin-1/2 layer through well-defined quantum emission operation. We show that the underlying Markov dynamics caputure maximal entanglement through the use of significant channels relevant to the AKLT state. We also show that SPT order induces a covariance on the observation decoding channels. This establishes an additional bridge between the quantum Machine learning and many-body physics, with promising implication in topological order and quantum information.