Weight Re-Mapping for Variational Quantum Algorithms

Inspired by the remarkable success of artificial neural networks across a broad spectrum of AI tasks, variational quantum circuits (VQCs) have recently seen an upsurge in quantum machine learning applications. The promising outcomes shown by VQCs, such as improved generalization and reduced parameter training requirements, are attributed to the robust algorithmic capabilities of quantum computing. However, the current gradient-based training approaches for VQCs do not adequately accommodate the fact that trainable parameters (or weights) are typically used as angles in rotational gates. To address this, we extend the concept of weight re-mapping for VQCs, as introduced by K\"olle et al. (2023). This approach unambiguously maps the weights to an interval of length $2\pi$, mirroring data rescaling techniques in conventional machine learning that have proven to be highly beneficial in numerous scenarios. In our study, we employ seven distinct weight re-mapping functions to assess their impact on eight classification datasets, using variational classifiers as a representative example. Our results indicate that weight re-mapping can enhance the convergence speed of the VQC. We assess the efficacy of various re-mapping functions across all datasets and measure their influence on the VQC's average performance. Our findings indicate that weight re-mapping not only consistently accelerates the convergence of VQCs, regardless of the specific re-mapping function employed, but also significantly increases accuracy in certain cases.

Improving Convergence for Quantum Variational Classifiers using Weight Re-Mapping

In recent years, quantum machine learning has seen a substantial increase in the use of variational quantum circuits (VQCs). VQCs are inspired by artificial neural networks, which achieve extraordinary performance in a wide range of AI tasks as massively parameterized function approximators. VQCs have already demonstrated promising results, for example, in generalization and the requirement for fewer parameters to train, by utilizing the more robust algorithmic toolbox available in quantum computing. A VQCs' trainable parameters or weights are usually used as angles in rotational gates and current gradient-based training methods do not account for that. We introduce weight re-mapping for VQCs, to unambiguously map the weights to an interval of length $2\pi$, drawing inspiration from traditional ML, where data rescaling, or normalization techniques have demonstrated tremendous benefits in many circumstances. We employ a set of five functions and evaluate them on the Iris and Wine datasets using variational classifiers as an example. Our experiments show that weight re-mapping can improve convergence in all tested settings. Additionally, we were able to demonstrate that weight re-mapping increased test accuracy for the Wine dataset by $10\%$ over using unmodified weights.