Quantum Dynamic Time Warping for Multivariate Time Series Classification

2026-06-26

AI Summary

This work addresses the limitation of traditional dynamic time warping (DTW), which relies on Euclidean distance and struggles to capture cross-channel dependencies in multivariate time series. The authors propose a hybrid quantum DTW (qDTW) framework that replaces classical distance with a parameterized geometric structure in a quantum Hilbert space, enabling efficient alignment via dynamic programming. A key innovation is the introduction of a unified pre-embedding ansatz that decouples trainable entanglement from classical inputs, thereby avoiding phase ambiguity and information bottlenecks. The study also uncovers a trade-off governing spatiotemporal expressivity, offering design principles for multivariate quantum circuits. Experiments demonstrate that qDTW outperforms classical baselines on multivariate time series benchmarks up to eight dimensions, validating the high representational power of untrained quantum kernels and their efficacy in disentangling high-dimensional overlapping data.

Abstract

Dynamic Time Warping (DTW) is a cornerstone for time series classification, but its reliance on Euclidean distances fails to capture latent cross-channel correlations in complex multivariate data. We propose a hybrid Quantum Dynamic Time Warping (qDTW) architecture, replacing the classical distance metric with the parameterized geometry of a quantum Hilbert space. Through structural ablation on benchmarks up to $C=8$ spatial dimensions, we establish fundamental topological rules for quantum sequence alignment. We introduce a Unified Pre-Embedding Adjoint Ansatz that decouples trainable entanglement from classical data, eliminating the severe phase-scrambling and information bottlenecks inherent to traditional measurements. We demonstrate this decoupled architecture allows untrained quantum kernels to act as highly expressive baselines, while parameterized training effectively untangles deeply overlapping hyper-dimensional data. Furthermore, we identify a strict spatial-temporal expressivity tradeoff: temporal depth (data re-uploading) is necessary for dimensionally restricted univariate circuits, but applying it to wide multi-qubit registers triggers chaotic frequency-spectrum explosions and representation collapse. By navigating these topological hazards, our multivariate quantum architecture outperforms classical baselines, setting a new standard for integrating parameterized quantum circuits with dynamic programming

Problem

• Dynamic Time Warping
• Multivariate Time Series
• Quantum Hilbert Space
• Cross-channel Correlations
• Time Series Classification

Innovation

• Quantum Dynamic Time Warping
• parameterized quantum circuits
• multivariate time series
• quantum kernel
• entanglement decoupling