Weight Re-Mapping for Variational Quantum Algorithms
Michael Kölle Alessandro Giovagnoli Jonas Stein Maximilian Balthasar Mansky Julian Hager Tobias Rohe Robert Müller Claudia Linnhoff-Popien
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.