qcnn-rough-path-signature

name	qcnn-rough-path-signature
description	Hybrid quantum-classical architecture combining path signature kernels with QCNN for time series classification, addressing time reparameterization invariance. (arXiv: 2607.07634)

QCNN with Rough Path Signature Kernels

Overview

This paper proposes a hybrid quantum-classical architecture integrating Quantum Convolutional Neural Networks (QCNN) with rough path signature kernels for time series classification. The approach mitigates time reparameterization invariance — a major challenge in time series analysis.

Paper: "QCNN with Rough Path Signature Kernels" (arXiv:2607.07634, 2026-07-08)

Core Methodology

Architecture

1. Signature Kernel Layer: Computes kernel between input path and reference path using classical or quantum VQLS
2. QCNN Layer: Performs downstream classification on signature features

Rough Path Signatures

Path signatures capture sequential information in a time-reparameterization invariant way. For a time series path X(t), the signature is the infinite sequence of iterated integrals:

• Level 1: ∫dX (total displacement)
• Level 2: ∫∫dX⊗dX (area swept)
• Level n: n-fold iterated integrals

Quantum Integration

• VQLS: Variational Quantum Linear Solver for computing signature kernels
• QCNN: Quantum convolutional layers for hierarchical feature extraction
• Tested on binary classification of handwritten digit time series

Implementation Pattern

def signature_kernel_layer(path_x, path_y, method="classical"):
    """Compute signature kernel between paths"""
    if method == "classical":
        return classical_signature_kernel(path_x, path_y)
    elif method == "quantum":
        # Use VQLS to solve linear system for kernel
        return vqls_signature_kernel(path_x, path_y)

def qcnn_signature_classifier(time_series, reference_paths):
    """Full pipeline: signature → QCNN → classification"""
    # Compute signature features
    features = [signature_kernel_layer(ts, ref) 
                for ref in reference_paths]
    # QCNN classification
    return qcnn_forward(features)

Key Findings

• Path signature kernels provide time-reparameterization invariance
• QCNN architectures can leverage signature features effectively
• VQLS implementation faces computational limitations at scale
• Classical signature kernel computation is more practical for current hardware

Pitfalls

• VQLS limitations: Variational quantum linear solvers face scalability challenges
• Truncation depth: Signature computation requires truncation; deeper truncation increases computational cost
• Reference path selection: Choice of reference paths affects kernel quality
• Quantum advantage unclear: Classical signatures may be sufficient for many practical applications

References

• arXiv:2607.07634 — QCNN with Rough Path Signature Kernels