Learning symmetry-protected topological order from trapped-ion experiments

TL;DR

This paper presents an unsupervised tensorial kernel support vector machine approach to identify symmetry-protected topological phases in trapped-ion quantum experiments, demonstrating robustness against noise.

Contribution

The work introduces a novel, interpretable machine learning method for analyzing quantum phases directly from experimental data without prior training.

Findings

Successfully distinguished SPT and trivial phases in noisy trapped-ion data.

Applied the method to both qubit and qutrit systems with consistent results.

Demonstrated robustness of the approach across different experimental setups.

Abstract

Classical machine learning has proven remarkably useful in post-processing quantum data, yet typical learning algorithms often require prior training to be effective. In this work, we employ a tensorial kernel support vector machine (TK-SVM) to analyze experimental data produced by trapped-ion quantum computers. This unsupervised method benefits from directly interpretable training parameters, allowing it to identify the non-trivial string-order characterizing symmetry-protected topological (SPT) phases. We apply our technique to two examples: a spin-1/2 model and a spin-1 model, featuring the cluster state and the AKLT state as paradigmatic instances of SPT order, respectively. Using matrix product states, we generate a family of quantum circuits that host a trivial phase and an SPT phase, with a sharp phase transition between them. For the spin-1 case, we implement these circuits on two distinct trapped-ion machines based on qubits and qutrits. Our results demonstrate that the TK-SVM method successfully distinguishes the two phases across all noisy experimental datasets, highlighting its robustness and effectiveness in quantum data interpretation.