Hybrid Quantum-Classical Architecture Using Path Signature Kernels for Time Series Classification

This paper proposes a hybrid quantum-classical architecture for time series classification that integrates Quantum Convolutional Neural Networks (QCNN) with rough path signature kernels. The architecture addresses the challenge of time reparameterization invariance in time series data by using feature layers that compute signature kernels between input paths, employing either classical or quantum variational linear solvers (VQLS). These feature layers feed into a QCNN for downstream learning tasks. The authors evaluate multiple QCNN configurations on a binary classification task using time series representations of handwritten digits, demonstrating potential advantages of implementing path signature kernel layers within quantum circuits while also analyzing computational limitations of the VQLS component.