Add quantum kernel pre-screening demo based on Huang et al. #1569
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Hi @daniela-angulo , I checked the preview and some things did not render properly, do I need to do anything? |
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Hi @andynader, yeah, I saw that. |
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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? |
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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? |
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Yes, I think we could probably do that. |
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? |
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I will also work on making the figures smaller this weekend and push the changes |
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Hi! |
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Such a cool demo, the main idea is clearly well presented.
I only added a few comments. Thanks!
| 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. | ||
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| Huang *et al.* (https://arxiv.org/abs/2011.01938) introduced exactly this test. Their proposed |
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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
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Is the best way to incorporate this directly into the demo file, put the reference here, or in the notebook and then convert again?
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best to do it in the demo file directly. If you run into difficulties, let me know, and I'll help.
| # :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) |
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I think we might leave this out since it is repeated from the above equations. Just to shorten up the demo a bit.
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No problem. Should I update myself?
Co-authored-by: Daniela Angulo <42325731+daniela-angulo@users.noreply.github.com>
Co-authored-by: Daniela Angulo <42325731+daniela-angulo@users.noreply.github.com>
Co-authored-by: Daniela Angulo <42325731+daniela-angulo@users.noreply.github.com>
Co-authored-by: Daniela Angulo <42325731+daniela-angulo@users.noreply.github.com>
Co-authored-by: Daniela Angulo <42325731+daniela-angulo@users.noreply.github.com>
Co-authored-by: Daniela Angulo <42325731+daniela-angulo@users.noreply.github.com>
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Thanks for your hard work @daniela-angulo, I committed the suggestions, hope this didn't break anything. What's left is to make the figures smaller, and include the changes in my replies to your comments. Can I pull the latest changes and update myself? |
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Thanks for reviewing this, @andynader . Yes, you can update the changes yourself and commit them to the repo. |
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Hi, I wanted to let you know I will be away for the next three weeks. I will continue working on the demo once I am back. Thank you! |
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Absolutely, thank you for your hard work Daniela! |
demonstrations_v2/huang_geometric_kernel_difference/metadata.json
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| from sklearn.metrics.pairwise import rbf_kernel | ||
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| # ---------------------------------------------------------------------------# | ||
| # Classical RBF Gram matrix # | ||
| # ---------------------------------------------------------------------------# | ||
| def classical_rbf_kernel(X, gamma=1.0): | ||
| return rbf_kernel(X, gamma=gamma) | ||
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| K_classical = classical_rbf_kernel(X_train) | ||
| print(f"K_RBF shape: {K_classical.shape}") | ||
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| # ---------------------------------------------------------------------------# | ||
| # Quantum fidelity-based Gram matrices # | ||
| # ---------------------------------------------------------------------------# | ||
| dev = qml.device("default.qubit", wires=n_qubits, shots=None) | ||
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| def overlap_prob(x, y, embed): | ||
| """Probability of measuring |0…0⟩ after U(x) U†(y).""" | ||
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| @qml.qnode(dev) | ||
| def circuit(): | ||
| embed(x) | ||
| qml.adjoint(embed)(y) | ||
| return qml.probs(wires=range(n_qubits)) | ||
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| return circuit()[0] | ||
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| def quantum_kernel_matrix(X, embed): | ||
| return qml.kernels.kernel_matrix(X, X, lambda v1, v2: overlap_prob(v1, v2, embed)) | ||
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| print("Computing QK-E1 (fidelity)...") | ||
| K_quantum_E1 = quantum_kernel_matrix(X_train, embed=embedding_E1) | ||
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| print("Computing QK-E2 (fidelity)...") | ||
| K_quantum_E2 = quantum_kernel_matrix(X_train, embed=embedding_E2) | ||
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| print(f"K_QK_E1 shape: {K_quantum_E1.shape}") | ||
| print(f"K_QK_E2 shape: {K_quantum_E2.shape}") | ||
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| # ---------------------------------------------------------------------------# | ||
| # Projected quantum kernels (Pauli vectors + classical RBF) # | ||
| # ---------------------------------------------------------------------------# | ||
| def get_pauli_vectors(embedding_func, X): | ||
| """Returns Pauli expectation vectors for each input using the given embedding.""" | ||
| observables = [] | ||
| for i in range(n_qubits): | ||
| observables.extend([qml.PauliX(i), qml.PauliY(i), qml.PauliZ(i)]) | ||
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| @qml.qnode(dev) | ||
| def pauli_qnode(x): | ||
| embedding_func(x) | ||
| return [qml.expval(obs) for obs in observables] | ||
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| vectors = [pauli_qnode(x) for x in X] | ||
| return np.array(vectors) | ||
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| def calculate_gamma(vectors): | ||
| """Use heuristic gamma = 1 / (d * var) for RBF kernel on Pauli space.""" | ||
| d = vectors.shape[1] | ||
| var = np.var(vectors) | ||
| return 1.0 / (d * var) if var > 1e-8 else 1.0 | ||
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| def pqk_kernel_matrix(X, embedding_func): | ||
| """Computes PQK kernel matrix from Pauli vectors + RBF kernel.""" | ||
| pauli_vecs = get_pauli_vectors(embedding_func, X) | ||
| gamma = calculate_gamma(pauli_vecs) | ||
| return rbf_kernel(pauli_vecs, gamma=gamma) | ||
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| print("Computing PQK-E1 (Pauli + RBF)...") | ||
| K_pqk_E1 = pqk_kernel_matrix(X_train, embedding_E1) | ||
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| print("Computing PQK-E2 (Pauli + RBF)...") | ||
| K_pqk_E2 = pqk_kernel_matrix(X_train, embedding_E2) | ||
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| print(f"K_PQK_E1 shape: {K_pqk_E1.shape}") | ||
| print(f"K_PQK_E2 shape: {K_pqk_E2.shape}") |
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this block of code is quite long, is there a possibility to break it into two?
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Hi @andynader ! As you can probably tell, I am back :D |
2 participants
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:
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?