Quantum support vector machines for classification and regression on a trapped-ion quantum computer

TL;DR

This paper demonstrates the use of a shallow quantum kernel on a trapped-ion quantum computer for classification and regression tasks, showing comparable performance to noiseless simulations and robustness to noise.

Contribution

It introduces a practical implementation of quantum support vector machines on a trapped-ion quantum computer, analyzing noise effects and proposing low-rank approximations to improve regression performance.

Findings

Quantum kernels are effective for classification and regression on noisy hardware.

Performance on a 4-qubit trapped-ion device is comparable to noiseless simulations.

Low-rank approximation improves regression accuracy on noisy quantum devices.

Abstract

Quantum machine learning is a rapidly growing field at the intersection of quantum computing and machine learning. In this work, we examine our quantum machine learning models, which are based on quantum support vector classification (QSVC) and quantum support vector regression (QSVR). We investigate these models using a quantum-circuit simulator, both with and without noise, as well as the IonQ Harmony quantum processor. For the QSVC tasks, we use a dataset containing fraudulent credit card transactions and image datasets (the MNIST and the Fashion-MNIST datasets); for the QSVR tasks, we use a financial dataset and a materials dataset. For the classification tasks, the performance of our QSVC models using 4 qubits of the trapped-ion quantum computer was comparable to that obtained from noiseless quantum-circuit simulations. The result is consistent with the analysis of our device-noise simulations with varying qubit-gate error rates. For the regression tasks, applying a low-rank approximation to the noisy quantum kernel, in combination with hyperparameter tuning in {\epsilon}-SVR, improved the performance of the QSVR models on the near-term quantum device. The alignment, as measured by the Frobenius inner product between the noiseless and noisy quantum kernels, can serve as an indicator of the relative prediction performance on noisy quantum devices in comparison with their ideal counterparts. Our results suggest that the quantum kernel, as described by our shallow quantum circuit, can be effectively used for both QSVC and QSVR tasks, indicating its resistance to noise and its adaptability to various datasets.