qcnn-rough-path-signatures

name	qcnn-rough-path-signatures
description	Quantum Convolutional Neural Network with Rough Path Signature Kernels for time series classification. Hybrid quantum-classical architecture using path signatures to handle time reparameterization invariance.
tags	["quantum","neural-network","time-series","path-signatures","qcnn","variational-quantum"]
created	2026-07-09T00:00:00.000Z

QCNN with Rough Path Signature Kernels

Overview

Hybrid quantum-classical architecture for time series classification that integrates Quantum Convolutional Neural Networks (QCNN) with rough path signature kernels to address time reparameterization invariance.

Core Methodology

Path Signature Kernels

• Computes signature kernel between pairs of input paths (reference path vs target path)
• Mitigates impact of time reparametrization invariance in time series data
• Feature layers use either classical or quantum variational linear solvers (VQLS)

Architecture Components

1. Signature Kernel Layer: Computes path signatures using classical or quantum VQLS
2. QCNN Layer: Performs downstream learning tasks with quantum convolutional operations
3. Hybrid Integration: Classical preprocessing + quantum feature extraction + quantum classification

Key Innovations

• First application of rough path theory to quantum neural networks
• Handles time warping/reparameterization without explicit alignment
• Leverages quantum advantage for high-dimensional feature spaces

Implementation Details

Signature Kernel Computation

For input paths X, Y:
1. Compute iterated integrals (signature) up to depth N
2. Inner product in signature space: <S(X), S(Y)>
3. Use as kernel for quantum circuit encoding

Quantum Circuit Design

• Variational quantum linear solver (VQLS) for signature computation
• QCNN architecture with pooling layers for hierarchical feature extraction
• Parameterized quantum circuits for classification

Applications

• Time series classification with temporal warping
• Handwritten digit recognition from temporal sequences
• Any sequential data with reparameterization invariance

Limitations

• VQLS component has computational limitations for deep signatures
• Requires careful choice of signature truncation depth
• Quantum hardware constraints on circuit depth

Activation Keywords

quantum CNN, rough paths, signature kernels, time series classification, VQLS, path signatures, temporal invariance, quantum neural networks

Reference

arXiv:2607.07634 - "QCNN with Rough Path Signature Kernels"