IQGO: Iterative Quantum Gate Optimiser for Quantum Data Embedding

Quantum kernel methods and Variational Quantum Classifiers (VQCs) have recently gained significant interest in the field of Machine Learning (ML). They have the potential to achieve superior generalisation whilst using smaller datasets and fewer parameters compared to their classical counterparts. However, kernel methods which leverage feature map embedding, often struggle with overfitting, which compromises their generalisation performance on unseen data. VQCs which utilise Parameterised Quantum Circuits (PQCs) to model the relationship between input data and the output, are susceptible to the Barren Plateau (BP) problem. To address these challenges, we introduce an adaptive quantum embedding optimisation algorithm, namely the Iterative Quantum Gate Optimiser (IQGO), which is suited to the task of tabular data classification. IQGO employs a Greedy Search algorithm to optimise the quantum embedding. Empirical evidence on noiseless simulations show that it addresses both the overfitting and the BP problem. We demonstrate the efficacy of IQGO on simulations of 21 qubits for the quantum kernel and 4 qubits for the VQC. Using small tabular datasets, we benchmark our approach against contemporary state-of-the-art classical algorithms. These promising results suggest that quantum algorithms may perform well at data classification problems. We test 5 binary classification problems and show that in 3 of them the IQGO algorithm admits competitive or better performance in terms of generalisation than existing state-of-the-art algorithms.