Add demo: geometric kernel distance applications from Huang et al.

[andynader]

Title: Add demo: geometric kernel distance applications from Huang et al.

Summary: This demo explores the geometric kernel distance (g-metric) from Huang et al.'s work as a tool for evaluating whether quantum kernels offer advantages over classical kernels for specific datasets. Uses the "two-moons" dataset to demonstrate a practical "g-first" approach to quantum kernel evaluation.

Relevant references: Huang et al. - Power of Data in Quantum Machine Learning

Possible Drawbacks: None identified

Related GitHub Issues: None

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GOALS: Demonstrate practical application of the g-metric for quantum kernel evaluation, showing PennyLane implementation of recent theoretical work.

AUDIENCE: Machine learning researchers interested in quantum kernels, practitioners evaluating quantum vs classical approaches.

KEYWORDS: quantum kernels, geometric difference, kernel methods, quantum machine learning, g-metric

Documentation type:

• Tutorial
• Demo
• How-to

Thumbnail Description

Left: Classical computing symbol (circuit board/binary). Right: Quantum symbol (atom/Bloch sphere). Center: Large "g" with question mark. Bottom text: "Is Your Quantum Kernel Worth It?" Clean, modern style with PennyLane brand colors. Concept: Classical vs quantum comparison through the g metric.

Additional Context

I've been working with Ben Lau on this demo and have received initial feedback. Ready for content team review.

[CatalinaAlbornoz]

Thank you for submitting this demo @andynader !

Our content team will review and come back with next steps. Do you have a specific deadline for the publication of this demo? We have several demos in the pipeline so it's useful for us to know if there's a specific date we need to meet.

[andynader]

Hi @CatalinaAlbornoz, no deadline at all, take your time :)