Add Figure 2 QNTK diagnostics reproduction

docs/source/public/reproduce/data.json

@@ -229,6 +229,51 @@
     "artifacts": [],
     "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_finite_temperature_lanczos"
   },
+  {
+    "slug": "2025_qntk_diagnostics",
+    "title": "Towards Practical Quantum Neural Network Diagnostics with Neural Tangent Kernels",
+    "card_title": "Figure 2 · QNTK diagnostics",
+    "summary": "QNTK spectra distinguish trainable low-frequency circuits from expressive high-frequency circuits that overfit TFIM data.",
+    "description": "Reproduces the visible part of all four Figure 2 panels for the paper's 6-qubit TFIM regression task, four QNN architectures, depths 5 through 30, and three fixed random initializations. The scope is limited to the portion visible on the paper's approximately 620-parameter axis. The VQE targets are digitized from the manuscript's vector dataset figure because the underlying table is not published. The model output is the representative first-qubit transverse-X expectation required by the TFIM target. The paper also omits an explicit feature-to-rotation-angle conversion; this reproduction uses pi times the scaled feature as an explicit reconstruction choice. The script supports comparable JAX and PyTorch runs through TensorCircuit-NG backend transforms.",
+    "authors": [
+      "Francesco Scala",
+      "Christa Zoufal",
+      "Dario Gerace",
+      "Francesco Tacchino"
+    ],
+    "contributor": "ninjaduck7",
+    "year": 2025,
+    "arxiv_id": "2503.01966",
+    "url": "https://arxiv.org/abs/2503.01966",
+    "tags": [
+      "quantum-machine-learning",
+      "variational-algorithm",
+      "many-body-physics"
+    ],
+    "tc_features": [
+      "circuit",
+      "expectation",
+      "jit",
+      "vmap",
+      "autodiff"
+    ],
+    "backend": "pytorch",
+    "hardware": {
+      "gpu": false,
+      "min_memory": "4GB"
+    },
+    "figures": [
+      {
+        "target": "Figure 2: QNTK spectrum, conditioning, and generalization diagnostics",
+        "source": "outputs/result.png",
+        "figure": "figures/2025_qntk_diagnostics__result.webp",
+        "thumb": "thumbs/2025_qntk_diagnostics__result.webp",
+        "script": "main.py"
+      }
+    ],
+    "artifacts": [],
+    "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2025_qntk_diagnostics"
+  },
   {
     "slug": "2021_quantum_continual_learning",
     "title": "Quantum Continual Learning Overcoming Catastrophic Forgetting",