Add quantum kernel pre-screening demo based on Huang et al. #1569

andynader · 2025-10-06T20:18:45Z

Title:
Before You Train: Pre-screening Quantum Kernels with Geometric Difference

Summary:
This demo implements the geometric difference metric (g) from Huang et al. (2021) for pre-screening quantum kernels before training. The metric quantifies how differently a quantum kernel's geometry represents data compared to a classical kernel, allowing practitioners to identify promising quantum approaches early and avoid wasting time on kernels with no potential advantage. Using synthetic two-moons data, we demonstrate how to calculate g for multiple quantum kernel variants (fidelity-based and projected) and interpret the results to guide kernel selection.

Relevant references:

Huang et al., "Power of data in quantum machine learning" (2021) - https://arxiv.org/abs/2011.01938

Possible Drawbacks:
None

Related GitHub Issues:
None

GOALS — Why are we working on this now?
Provide practitioners with a practical tool for quantum kernel evaluation. Address a common pain point where researchers spend significant time tuning quantum kernels that fundamentally cannot outperform classical ones.

AUDIENCE — Who is this for?
QML researchers and practitioners working with quantum kernels, ML engineers exploring quantum advantages, and anyone interested in practical quantum machine learning workflows.

KEYWORDS:
quantum kernels, geometric difference, pre-screening, kernel methods, SVM, quantum machine learning, quantum advantage

Which type of documentation?

Tutorial
Demo
How-to

this is for validation and make a preview

github-actions · 2025-10-06T20:42:01Z

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Deployed at: 2025-10-20 21:45:50 UTC

andynader · 2025-10-06T23:09:53Z

Hi @daniela-angulo , I checked the preview and some things did not render properly, do I need to do anything?

daniela-angulo · 2025-10-07T13:52:00Z

Hi @andynader, yeah, I saw that.
Not for now, let me try to fix a few things and I'll loop you in when I have finished the demo so you can address all the suggestions and/or changes at once.
Thanks.

daniela-angulo · 2025-10-07T19:49:27Z

Hi @andynader, I think I addressed all the formatting issues. Could you verify that for me? Is the demo looking the way it is intended to?
I have not yet reviewed it, but I will this week. However, I noted a few things in the PR as comments regarding two figures. We can start with these two things and then move forward to the review when I get to it.
Thank you!

demonstrations_v2/huang_geometric_kernel_difference/demo.py

… layout

andynader · 2025-10-09T19:13:05Z

Hi Daniela, thank you for your hard work. I changed the code as you recommended; should we also make some figures such as the scatter plot and embedding circuit plots smaller or do you think they're good?

daniela-angulo · 2025-10-14T21:25:47Z

Yes, I think we could probably do that.
Have you started discussing the graphics with Ben?
Thanks @andynader !

andynader · 2025-10-17T19:47:05Z

Yes, I think we could probably do that. Have you started discussing the graphics with Ben? Thanks @andynader !

Hi Daniela, yes he told me you have an in house graphic designer who can make them, how should I move forward? Should I contact Ben?

andynader · 2025-10-17T19:48:33Z

I will also work on making the figures smaller this weekend and push the changes

daniela-angulo · 2025-10-17T20:19:09Z

Hi!
yes, please. You can contact Ben over email and he'll help us with that.
Thank you.
I will review the demo from a more content/science perspective next week.

daniela-angulo

Such a cool demo, the main idea is clearly well presented.
I only added a few comments. Thanks!

daniela-angulo · 2025-10-21T13:56:39Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

@@ -0,0 +1,773 @@
+r"""Is a Quantum Kernel Worth Exploring? A ‘:math:`g`-first’ Reality Check


is this your preferred title or the on in the metadata file? they are different

daniela-angulo · 2025-10-21T14:14:49Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

+From a practitioner’s perspective, such a **pre-screening test** is invaluable: it lets us rule out
+quantum kernels that don’t offer any potential quantum advantage right from the start.
+
+Huang *et al.* (https://arxiv.org/abs/2011.01938) introduced exactly this test. Their proposed


we should have a reference section at the end, before the appendix. It doesn't matter if all we cite is the same article several times.
You can take a look at other demos in the open PRs in the repo #1577

daniela-angulo · 2025-10-21T14:16:14Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

+
+3. **Our approach**: Calculate :math:`g` values between the classical kernel and each quantum
+   kernel—giving us an immediate assessment of which quantum approaches might be worth pursuing
+   across any kernel-based method


Suggested change

across any kernel-based method

across any kernel-based method.

daniela-angulo · 2025-10-21T14:16:22Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

+Demonstration setup:
+--------------------
+
+1. **Dataset**: Synthetic two-moons data generated with ``scikit-learn``


Suggested change

1. **Dataset**: Synthetic two-moons data generated with ``scikit-learn``

1. **Dataset**: Synthetic two-moons data generated with ``scikit-learn``.

daniela-angulo · 2025-10-21T14:41:36Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

+# :math:`K_{\text{RBF}}` obtained from:
+#
+# .. math:: k_{\text{RBF}}(x, x') = \exp(-\gamma \|x - x'\|^2)
+#
+# :math:`K_{\text{QK-E1}}` obtained from:
+#
+# .. math:: k_{\text{QK-E1}}(x, x') = |\langle \psi_{\text{E1}}(x) \mid \psi_{\text{E1}}(x') \rangle|^2
+#
+# :math:`K_{\text{QK-E2}}` obtained from:
+#
+# .. math:: k_{\text{QK-E2}}(x, x') = |\langle \psi_{\text{E2}}(x) \mid \psi_{\text{E2}}(x') \rangle|^2
+#
+# :math:`K_{\text{PQK-E1}}` obtained from:
+#
+# .. math:: k_{\text{PQK-E1}}(x, x') = \exp\left( -\gamma \|v_{\text{E1}}(x) - v_{\text{E1}}(x')\|^2 \right)
+#
+# :math:`K_{\text{PQK-E2}}` obtained from:
+#
+# .. math:: k_{\text{PQK-E2}}(x, x') = \exp\left( -\gamma \|v_{\text{E2}}(x) - v_{\text{E2}}(x')\|^2 \right)


I think we might leave this out since it is repeated from the above equations. Just to shorten up the demo a bit.

daniela-angulo · 2025-10-21T14:42:38Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

+# Each entry :math:`K_{ij}` measures how similar two data points are, and the full matrix :math:`K`
+# provides a **global view** of the data in the kernel’s feature space.
+#
+# We compute five such matrices, one for each kernel defined above:


Suggested change

# We compute five such matrices, one for each kernel defined above:

# We compute five such matrices, one for each kernel defined above.

daniela-angulo · 2025-10-21T14:43:56Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

+#
+# This intuition is understandable — after all, a larger :math:`g` suggests that the quantum kernel
+# perceives the data very differently from a classical one.
+# But as we’ll see, **a higher :math:`g` doesn’t always translate into better accuracy, it just


Suggested change

# But as we’ll see, **a higher :math:`g` doesn’t always translate into better accuracy, it just

# But as we’ll see, **a higher** :math:`g` **doesn’t always translate into better accuracy, it just

the math mode doesn't render within bolded font

daniela-angulo · 2025-10-21T14:47:57Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

+# - The role of :math:`g` is *not* to predict which kernel will perform best on a given task, but
+#   rather to obtain a collection of kernels that have the *potential* to offer an advantage.
+#
+# Here, PQK-E1 and PQK-E2 both had the potential for an advantage over classical, but PQK-E2 is the


over classical kernels or classical ...?

daniela-angulo · 2025-10-21T14:48:43Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

+# potential solution because it offers a potential for an improvement on our classification problem.
+# This way, we have an important diagnostic tool to filter out bad quantum kernels for our data.
+#
+# 🧠 Conclusion: A practical perspective on the Geometric difference :math:`g`


Suggested change

# 🧠 Conclusion: A practical perspective on the Geometric difference :math:`g`

# 🧠 Conclusion: A practical perspective on the Geometric difference g

daniela-angulo · 2025-10-21T14:49:06Z

demonstrations_v2/huang_geometric_kernel_difference/demo.py

+# **Can we anticipate, before training, whether a quantum kernel might outperform a classical
+# one?**
+#
+# To address this, we used the **geometric difference :math:`g`**, a pre-training metric introduced by


Suggested change

# To address this, we used the **geometric difference :math:`g`**, a pre-training metric introduced by

# To address this, we used the **geometric difference** :math:`g`, a pre-training metric introduced by

andynader and others added 2 commits October 6, 2025 16:12

Add quantum kernel pre-screening demo based on Huang et al.

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Update metadata.json

c228923

this is for validation and make a preview

daniela-angulo added 8 commits October 7, 2025 10:08

Update demo.py

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render quickly

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Update demo.py

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Update demo.py

4e87ef0

execute it again

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Update demo.py

441edb1

this should fix all the formatting issues

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Update demo.py

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daniela-angulo reviewed Oct 7, 2025

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daniela-angulo reviewed Oct 7, 2025

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Address reviewer feedback: add circuit titles and improve Gram matrix…

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… layout

Merge branch 'master' into quantum-kernel-prescreening

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formatting

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daniela-angulo reviewed Oct 21, 2025

View reviewed changes

		@@ -0,0 +1,773 @@
		r"""Is a Quantum Kernel Worth Exploring? A ‘:math:`g`-first’ Reality Check

	across any kernel-based method
	across any kernel-based method.

	1. Dataset: Synthetic two-moons data generated with ``scikit-learn``
	1. Dataset: Synthetic two-moons data generated with ``scikit-learn``.

	# We compute five such matrices, one for each kernel defined above:
	# We compute five such matrices, one for each kernel defined above.

	# But as we’ll see, **a higher :math:`g` doesn’t always translate into better accuracy, it just
	# But as we’ll see, a higher :math:`g` **doesn’t always translate into better accuracy, it just

	# 🧠 Conclusion: A practical perspective on the Geometric difference :math:`g`
	# 🧠 Conclusion: A practical perspective on the Geometric difference g

	# To address this, we used the geometric difference :math:`g`, a pre-training metric introduced by
	# To address this, we used the geometric difference :math:`g`, a pre-training metric introduced by

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