Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data

TL;DR

This paper demonstrates the application of fidelity quantum kernels to real-world and synthetic data, introduces a novel error mitigation method called Bit Flip Tolerance, and achieves large-scale quantum machine learning experiments with accuracy comparable to classical models.

Contribution

It presents a new error mitigation strategy for fidelity kernels, enabling practical quantum machine learning on large-scale devices and real-world data.

Findings

Achieved quantum classification accuracy up to 80% on real-world data with 40+ qubits.

Demonstrated largest quantum machine learning experiment on IBM devices with 156 qubits.

Bit Flip Tolerance significantly improves quantum kernel performance in practical scenarios.

Abstract

Fidelity quantum kernels have shown promise in classification tasks, particularly when a group structure in the data can be identified and exploited through a covariant feature map. In fact, there exist classification problems on which covariant kernels provide a provable advantage, thus establishing a separation between quantum and classical learners. However, their practical application poses two challenges: on one side, the group structure may be unknown and approximate in real-world data, and on the other side, scaling to the `utility' regime (above 100 qubits) is affected by exponential concentration. In this work, we address said challenges by applying fidelity kernels to real-world data with unknown structure, related to the scheduling of a fleet of electric vehicles, and to synthetic data generated from the union of subspaces, which is then close to many relevant real-world datasets. Furthermore, we propose a novel error mitigation strategy specifically tailored for fidelity kernels, called Bit Flip Tolerance (BFT), to alleviate the exponential concentration in our utility-scale experiments. Our multiclass classification reaches accuracies comparable to classical SVCs up to 156 qubits, thus constituting the largest experimental demonstration of quantum machine learning on IBM devices to date. For the real-world data experiments, the effect of the proposed BFT becomes manifest on 40+ qubits, where mitigated accuracies reach 80%, in line with classical, compared to 33% without BFT. Through the union-of-subspace synthetic dataset with 156 qubits, we demonstrate a mitigated accuracy of 80%, compared to 83% of classical models, and 37% of unmitigated quantum, using a test set of limited size.