Supervised binary classification of small-scale digit images and weighted graphs with a trapped-ion quantum processor

TL;DR

This paper benchmarks a trapped-ion quantum processor using quantum machine learning algorithms for binary classification of small digit images and weighted graphs, achieving perfect accuracy and demonstrating quantum advantage in basic classification tasks.

Contribution

It introduces the use of a trapped-ion quantum processor for supervised binary classification on small datasets, showing 100% accuracy and analyzing quantum encoding and noise effects.

Findings

Achieved 100% accuracy on small digit image classification.

Successfully classified weighted graphs based on spectral properties.

Demonstrated quantum processor's capability for basic machine learning tasks.

Abstract

Here we present the results of benchmarking a quantum processor based on trapped $^{171}$Yb$^{+}$ ions by performing basic quantum machine learning algorithms. Using a quantum-enhanced support vector machine algorithm with up to five qubits we perform a supervised binary classification on two types of datasets: small binary digit images and weighted graphs with a ring topology. For the first dataset, images are intentionally selected so that they could be classified with 100% accuracy. This allows us to specifically examine different types of quantum encodings of the digit dataset and study the impact of experimental noise. In the second dataset, graphs are divided into two categories based on the spectral structure of their Ising Hamiltonian models, which is related to the NP-hard problem. For this problem we consider an embedding of an exponentially large Hamiltonian spectrum into an entangled state of a linear number of qubits. For both problems, we study various levels of circuit optimization and found that, for all experiments conducted, we achieve classifiers with 100% accuracy on both training and testing datasets. This demonstrates that the quantum processor has the ability to correctly solve the basic classification task under consideration. As we expect, with the increase in the capabilities of quantum processors, they can be utilized for solving machine learning tasks.