Abstract
Time series analysis plays a vital role across a wide range of scientific and engineering domains but poses substantial computational challenges. A major difficulty arises from the time reparameterization invariance of time series data, complicating the extraction of meaningful temporal features. In this work, we address the problem of time series classification by exploring quantum computation techniques.
We propose a hybrid quantum-classical architecture that integrates recent advances in quantum neural networks with the mathematical framework of path signatures, mitigating the impact of time reparametrization invariance. The architecture employs feature layers that compute a signature kernel between pairs of input paths, consisting of a reference path and a target path for classification, using either classical or quantum variational linear solvers (VQLS).
These feature layers are followed by a Quantum Convolutional Neural Network (QCNN) to perform downstream learning tasks. We evaluate several realizations of the proposed architecture, differing in QCNN configurations, on a binary classification task involving time series representations of handwritten digits. Our experiments demonstrate the potential advantages of implementing path signature kernel layers within quantum circuits and provide an analysis of the computational limitations associated with the VQLS component.
Blogger's Review: This paper merges quantum computing with path signature kernels to propose a novel approach for time series classification, showcasing the potential of quantum technology in handling complex data structures. Particularly, it offers innovative solutions to the challenges posed by time series invariance, making it a noteworthy contribution to the field.