diff --git a/docs/source/public/reproduce/data.json b/docs/source/public/reproduce/data.json
index 6b1921cd..0768811b 100644
--- a/docs/source/public/reproduce/data.json
+++ b/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",
diff --git a/docs/source/public/reproduce/figures/2025_qntk_diagnostics__result.webp b/docs/source/public/reproduce/figures/2025_qntk_diagnostics__result.webp
new file mode 100644
index 00000000..5f4f4c0b
Binary files /dev/null and b/docs/source/public/reproduce/figures/2025_qntk_diagnostics__result.webp differ
diff --git a/docs/source/public/reproduce/index.html b/docs/source/public/reproduce/index.html
index ea26ccf7..4fe73bab 100644
--- a/docs/source/public/reproduce/index.html
+++ b/docs/source/public/reproduce/index.html
@@ -355,11 +355,11 @@ <h1>Quantum Research, <span class="gradient-text">Made Executable</span></h1>
     </div>
     <div class="facet">
       <span class="facet-label">Topic</span>
-      <button class="chip" type="button" data-facet="tags" data-value="quantum-machine-learning" aria-pressed="false">Quantum Machine Learning<span class="count">5</span></button>
+      <button class="chip" type="button" data-facet="tags" data-value="quantum-machine-learning" aria-pressed="false">Quantum Machine Learning<span class="count">6</span></button>
+          <button class="chip" type="button" data-facet="tags" data-value="variational-algorithm" aria-pressed="false">Variational Algorithm<span class="count">5</span></button>
           <button class="chip" type="button" data-facet="tags" data-value="classification" aria-pressed="false">Classification<span class="count">4</span></button>
+          <button class="chip" type="button" data-facet="tags" data-value="many-body-physics" aria-pressed="false">Many-Body Physics<span class="count">4</span></button>
           <button class="chip" type="button" data-facet="tags" data-value="tensor-network" aria-pressed="false">Tensor Network<span class="count">4</span></button>
-          <button class="chip" type="button" data-facet="tags" data-value="variational-algorithm" aria-pressed="false">Variational Algorithm<span class="count">4</span></button>
-          <button class="chip" type="button" data-facet="tags" data-value="many-body-physics" aria-pressed="false">Many-Body Physics<span class="count">3</span></button>
           <button class="chip" type="button" data-facet="tags" data-value="quantum-algorithm" aria-pressed="false">Quantum Algorithm<span class="count">3</span></button>
           <button class="chip" type="button" data-facet="tags" data-value="combinatorial-optimization" aria-pressed="false">Combinatorial Optimization<span class="count">2</span></button>
           <button class="chip" type="button" data-facet="tags" data-value="entanglement" aria-pressed="false">Entanglement<span class="count">2</span></button>
@@ -376,12 +376,12 @@ <h1>Quantum Research, <span class="gradient-text">Made Executable</span></h1>
     </div>
     <div class="facet">
       <span class="facet-label">TC feature</span>
-      <button class="chip" type="button" data-facet="features" data-value="jit" aria-pressed="false">JIT<span class="count">10</span></button>
-          <button class="chip" type="button" data-facet="features" data-value="circuit" aria-pressed="false">Circuit Simulation<span class="count">7</span></button>
-          <button class="chip" type="button" data-facet="features" data-value="vmap" aria-pressed="false">Vectorization<span class="count">6</span></button>
-          <button class="chip" type="button" data-facet="features" data-value="autodiff" aria-pressed="false">Automatic Differentiation<span class="count">5</span></button>
+      <button class="chip" type="button" data-facet="features" data-value="jit" aria-pressed="false">JIT<span class="count">11</span></button>
+          <button class="chip" type="button" data-facet="features" data-value="circuit" aria-pressed="false">Circuit Simulation<span class="count">8</span></button>
+          <button class="chip" type="button" data-facet="features" data-value="vmap" aria-pressed="false">Vectorization<span class="count">7</span></button>
+          <button class="chip" type="button" data-facet="features" data-value="autodiff" aria-pressed="false">Automatic Differentiation<span class="count">6</span></button>
+          <button class="chip" type="button" data-facet="features" data-value="expectation" aria-pressed="false">Expectation<span class="count">4</span></button>
           <button class="chip" type="button" data-facet="features" data-value="backend-api" aria-pressed="false">Backend API<span class="count">3</span></button>
-          <button class="chip" type="button" data-facet="features" data-value="expectation" aria-pressed="false">Expectation<span class="count">3</span></button>
           <button class="chip" type="button" data-facet="features" data-value="contractor" aria-pressed="false">Custom Contractor<span class="count">2</span></button>
           <button class="chip" type="button" data-facet="features" data-value="pauli-operator" aria-pressed="false">Pauli Operator<span class="count">2</span></button>
           <button class="chip" type="button" data-facet="features" data-value="scan" aria-pressed="false">Scan<span class="count">2</span></button>
@@ -391,7 +391,7 @@ <h1>Quantum Research, <span class="gradient-text">Made Executable</span></h1>
           <button class="chip" type="button" data-facet="features" data-value="sampling" aria-pressed="false">Sampling<span class="count">1</span></button>
     </div>
     <div class="statusbar">
-      <span id="count">13 reproductions</span>
+      <span id="count">14 reproductions</span>
       <button class="linkbtn" id="reset" type="button">reset filters</button>
     </div>
   </div>
@@ -479,6 +479,22 @@ <h3>Figure 1(a) · Thermal energy versus temperature</h3>
           <div class="taglist"><em>quantum-algorithm</em><em>finite-temperature</em><em>many-body-physics</em></div>
         </div>
       </article>
+      <article class="card" role="button" tabindex="0"
+        data-slug="2025_qntk_diagnostics"
+        data-title="Towards Practical Quantum Neural Network Diagnostics with Neural Tangent Kernels"
+        data-year="2025"
+        data-tags="quantum-machine-learning variational-algorithm many-body-physics"
+        data-features="circuit expectation jit vmap autodiff"
+        data-search="towards practical quantum neural network diagnostics with neural tangent kernels figure 2 · qntk diagnostics qntk spectra distinguish trainable low-frequency circuits from expressive high-frequency circuits that overfit tfim data. 2503.01966 2025_qntk_diagnostics pytorch francesco scala christa zoufal dario gerace francesco tacchino quantum-machine-learning variational-algorithm many-body-physics circuit expectation jit vmap autodiff">
+        <img class="shot" loading="lazy" src="thumbs/2025_qntk_diagnostics__result.webp" alt="Figure 2 · QNTK diagnostics">
+        <div class="body">
+          <h3>Figure 2 · QNTK diagnostics</h3>
+          <p class="paper">Towards Practical Quantum Neural Network Diagnostics with Neural Tangent Kernels</p>
+          <p class="summary">QNTK spectra distinguish trainable low-frequency circuits from expressive high-frequency circuits that overfit TFIM data.</p>
+          <div class="meta"><span>2025</span><span>Francesco Scala et al.</span><span>pytorch</span></div>
+          <div class="taglist"><em>quantum-machine-learning</em><em>variational-algorithm</em><em>many-body-physics</em></div>
+        </div>
+      </article>
       <article class="card" role="button" tabindex="0"
         data-slug="2021_quantum_continual_learning"
         data-title="Quantum Continual Learning Overcoming Catastrophic Forgetting"
@@ -625,7 +641,7 @@ <h3>Figure 6 · Topological quantum-walk edge state</h3>
 
 <div class="modal" id="modal" role="dialog" aria-modal="true"><div class="sheet" id="sheet"></div></div>
 
-<script id="gallery-data" type="application/json">[{"slug": "2026_qutrit_time_crystal", "title": "A Qutrit Time Crystal Stabilized with Native Chiral Interactions", "card_title": "Figure 2(b) · Qutrit time-crystal response", "summary": "A driven chiral clock model of 9 qutrits shows period-doubled magnetization and a sharp subharmonic peak in the Fourier spectrum.", "description": "Reproduces Figure 2(b) qualitatively with a noiseless TensorCircuit-NG and JAX simulation of the driven chiral clock model. The original 15-qutrit experiment is scaled to 9 qutrits for fast local execution, while keeping the same Floquet structure U_F = exp(-i H0) exp(-i Hint) X^g, disordered chiral couplings, the spin-1 magnetization observable M = |0><0| - |2><2|, and the DTC-versus-thermal comparison. The microwave kick is modeled as the fractional spectral power of the qutrit shift operator X^g, which is an explicit modeling simplification used to obtain a smooth noiseless interpolation away from the exact g = 1 kick.", "authors": ["Noah Goss", "Nishchay Suri", "Brian Marinelli", "Larry Chen", "Akel Hashim", "Sajant Anand", "Alexis Morvan", "Ravi K. Naik", "Ermal Rrapaj", "David I. Santiago", "Wibe de Jong", "Norman Y. Yao", "Joel E. Moore", "Irfan Siddiqi"], "contributor": "refraction-ray", "year": 2026, "arxiv_id": "2605.14293", "url": "https://arxiv.org/abs/2605.14293", "tags": ["qudit", "floquet-dynamics", "many-body-physics"], "tc_features": ["qudit-circuit", "jit"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Figure 2(b): Single-site magnetization traces and Fourier spectroscopy versus kick strength", "source": "outputs/result.png", "figure": "figures/2026_qutrit_time_crystal__result.webp", "thumb": "thumbs/2026_qutrit_time_crystal__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_qutrit_time_crystal"}, {"slug": "2026_diff_qec_surface", "title": "Differentiable Maximum Likelihood Noise Estimation for Quantum Error Correction", "card_title": "Noise estimation convergence", "summary": "Surface-code noise parameters are recovered by differentiating through a CopyNode tensor-network contraction and optimizing with Adam.", "description": "Reproducing the differentiable maximum likelihood noise estimation for surface code using Tensor Network contraction with CopyNodes. The paper reports no single target figure for this experiment, so the reproduction reports the optimization convergence of the estimated noise parameters.", "authors": ["Hanyan Cao", "Dongyang Feng", "Cheng Ye", "Feng Pan"], "contributor": "refraction-ray", "year": 2026, "arxiv_id": "2602.19722", "url": "https://arxiv.org/abs/2602.19722", "tags": ["quantum-error-correction", "tensor-network"], "tc_features": ["contractor", "jit", "vmap", "autodiff"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "8GB"}, "figures": [{"target": "Maximum-likelihood noise estimation convergence", "source": "outputs/convergence.png", "figure": "figures/2026_diff_qec_surface__convergence.webp", "thumb": "thumbs/2026_diff_qec_surface__convergence.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_diff_qec_surface"}, {"slug": "2026_sat_mps_entanglement", "title": "Entanglement Barriers from Computational Complexity: Matrix-Product-State Approach to Satisfiability", "card_title": "Figure 2 · Entanglement barrier in 3-SAT", "summary": "Imaginary-time propagation of hard 3-SAT instances shows the MPS entanglement entropy peaking near the satisfiability threshold.", "description": "Figure 2 reproduction using the authors' Zenodo protocol (10.5281/zenodo.18743084): Weigt hard-satisfiable 3-SAT generator with p0=0.08, violation-vector Hamiltonian, and continuous tau optimization in [0,7.5] with the same sample-rejection criterion f(7.5) > f(10.0). Scaled down to n=4-15 (Panel A), n=8-10 (Panel B), 200 instances for feasible runtimes while preserving the core physics (linear entropy scaling and alpha_c peak). The bipartite entropy is obtained from a singular value decomposition of the propagated state on the JAX backend rather than from a tc.MPSCircuit.", "authors": ["Tim Pokart", "Frank Pollmann", "Jan Carl Budich"], "contributor": "Qingyun Qian", "year": 2026, "arxiv_id": "2602.20299", "url": "https://arxiv.org/abs/2602.20299", "tags": ["matrix-product-state", "entanglement", "combinatorial-optimization", "tensor-network"], "tc_features": ["backend-api"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "4GB"}, "figures": [{"target": "Figure 2: (a) <S_hat> vs n at alpha_c, (b) <S_hat>/n vs alpha", "source": "outputs/result.png", "figure": "figures/2026_sat_mps_entanglement__result.webp", "thumb": "thumbs/2026_sat_mps_entanglement__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_sat_mps_entanglement"}, {"slug": "2026_quantum_oracle_sketching", "title": "Exponential Quantum Advantage in Processing Massive Classical Data", "card_title": "Figure 4(a) · Machine size versus accuracy", "summary": "Quantum oracle sketching is compared with classical streaming and sparse baselines on an MNIST 3-vs-8 task at matched accuracy.", "description": "Reproduces the Figure 4(a) machine-size versus accuracy trade-off on a binary MNIST task (digits 3 and 8, 2000 samples per class, full 28x28 images reduced by PCA), comparing classical streaming, classical sparse representations, and quantum oracle sketching. A second experiment verifies the sample-complexity theory behind Figure 3(a) by evaluating the expected sketching unitary for a random Boolean oracle on 6 qubits and comparing its operator-norm error against the theoretical O(N/M) bound. That second experiment is diagonal operator algebra written with tc.backend array operations rather than a gate-level tc.Circuit simulation.", "authors": ["Haimeng Zhao", "Alexander Zlokapa", "Hartmut Neven", "Ryan Babbush", "John Preskill", "Jarrod R. McClean", "Hsin-Yuan Huang"], "contributor": "refraction-ray", "year": 2026, "arxiv_id": "2604.07639", "url": "https://arxiv.org/abs/2604.07639", "tags": ["quantum-advantage", "quantum-machine-learning", "classification"], "tc_features": ["backend-api"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Figure 4(a) - Binary classification machine size vs accuracy", "source": "outputs/result.png", "figure": "figures/2026_quantum_oracle_sketching__result.webp", "thumb": "thumbs/2026_quantum_oracle_sketching__result.webp", "script": "main.py"}, {"target": "Figure 3(a) - Boolean oracle sketching error scaling vs O(N/M) bound", "source": "outputs/qos_scaling.png", "figure": "figures/2026_quantum_oracle_sketching__qos_scaling.webp", "thumb": "thumbs/2026_quantum_oracle_sketching__qos_scaling.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_quantum_oracle_sketching"}, {"slug": "2026_finite_temperature_lanczos", "title": "Quantum Finite Temperature Lanczos Method", "card_title": "Figure 1(a) · Thermal energy versus temperature", "summary": "Quantum Hutchinson states and a generalized eigenvalue problem give thermal energies of a 10-site TFIM without full diagonalization.", "description": "Reproduces thermal expectation values of energy for the Transverse-Field Ising Model using the Quantum Finite Temperature Lanczos Method (QFTLM). The original system size L=14 is scaled to L=10 for computational feasibility while maintaining the core algorithm logic (Quantum Hutchinson states and generalized eigenvalue problem).", "authors": ["Gian Gentinetta", "Friederike Metz", "William Kirby", "Giuseppe Carleo"], "contributor": "refraction-ray", "year": 2026, "arxiv_id": "2603.25394", "url": "https://arxiv.org/abs/2603.25394", "tags": ["quantum-algorithm", "finite-temperature", "many-body-physics"], "tc_features": ["pauli-operator", "jit", "vmap"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Figure 1(a): Thermal expectation of Energy <E> vs Temperature T", "source": "outputs/result.png", "figure": "figures/2026_finite_temperature_lanczos__result.webp", "thumb": "thumbs/2026_finite_temperature_lanczos__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_finite_temperature_lanczos"}, {"slug": "2021_quantum_continual_learning", "title": "Quantum Continual Learning Overcoming Catastrophic Forgetting", "card_title": "Figure 2(b) · Catastrophic forgetting", "summary": "An 8-qubit amplitude-encoded classifier trained sequentially on MNIST and permuted MNIST forgets the first task as it learns the second.", "description": "This reproduction demonstrates catastrophic forgetting in a quantum classifier by training sequentially on MNIST (0, 9) and permuted MNIST (0, 9). We use an 8-qubit variational quantum circuit with amplitude encoding and 10 layers of hardware-efficient gates, with the layer sweep expressed through tc.backend.scan.", "authors": ["Wenjie Jiang", "Zhide Lu", "Dong-Ling Deng"], "contributor": "refraction-ray", "year": 2021, "arxiv_id": "2108.02786", "url": "https://arxiv.org/abs/2108.02786", "tags": ["quantum-machine-learning", "classification", "variational-algorithm"], "tc_features": ["circuit", "jit", "vmap", "scan", "autodiff", "sampling"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "4GB"}, "figures": [{"target": "Figure 2(b)", "source": "outputs/result.png", "figure": "figures/2021_quantum_continual_learning__result.webp", "thumb": "thumbs/2021_quantum_continual_learning__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2021_quantum_continual_learning"}, {"slug": "2020_efficient_classical_simulation_random_shallow_2d", "title": "Efficient Classical Simulation of Random Shallow 2D Quantum Circuits", "card_title": "SEBD accuracy versus bond dimension", "summary": "Spatial Evolution Block Decimation contracts a random shallow 2D circuit as a PEPS-to-MPS sweep, checked against exact amplitudes.", "description": "This script implements the Spatial Evolution Block Decimation (SEBD) algorithm described in the paper for efficient classical simulation of random shallow 2D quantum circuits. Output amplitudes are compared against exact statevector amplitudes to quantify the truncation error as a function of the MPS bond dimension.", "authors": ["John Napp", "Rolando L. La Placa", "Alexander M. Dalzell", "Fernando G. S. L. Brandão", "Aram W. Harrow"], "contributor": "refraction-ray", "year": 2020, "arxiv_id": "2001.00021", "url": "https://arxiv.org/abs/2001.00021", "tags": ["classical-simulation", "tensor-network", "matrix-product-state", "random-circuit"], "tc_features": ["circuit"], "backend": "numpy", "hardware": {"gpu": false, "min_memory": "8GB"}, "figures": [{"target": "Accuracy comparison plot", "source": "outputs/accuracy.png", "figure": "figures/2020_efficient_classical_simulation_random_shallow_2d__accuracy.webp", "thumb": "thumbs/2020_efficient_classical_simulation_random_shallow_2d__accuracy.webp", "script": "main.py"}], "artifacts": ["outputs/results.log"], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2020_efficient_classical_simulation_random_shallow_2d"}, {"slug": "2019_data_reuploading", "title": "Data Re-uploading for a Universal Quantum Classifier", "card_title": "Figure 6 · Single-qubit universal classifier", "summary": "One qubit re-uploads the input at every layer to act as a universal classifier, trained with L-BFGS on the JAX backend.", "description": "Reproduces the single-qubit classifier experiment (Figure 6) using the data re-uploading technique, with the layer parameters optimized by optax L-BFGS.", "authors": ["Adrián Pérez-Salinas", "Alba Cervera-Lierta", "Elies Gil-Fuster", "José I. Latorre"], "contributor": "refraction-ray", "year": 2019, "arxiv_id": "1907.02085", "url": "https://arxiv.org/abs/1907.02085", "tags": ["quantum-machine-learning", "classification", "variational-algorithm"], "tc_features": ["circuit", "jit", "autodiff", "expectation"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "1GB"}, "figures": [{"target": "Figure 6", "source": "outputs/result.png", "figure": "figures/2019_data_reuploading__result.webp", "thumb": "thumbs/2019_data_reuploading__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2019_data_reuploading"}, {"slug": "2018_qcbm", "title": "Differentiable Learning of Quantum Circuit Born Machine", "card_title": "Figure 6 · QCBM learning a Gaussian mixture", "summary": "A 10-qubit hardware-efficient Born machine trained with an MMD loss to fit a Gaussian mixture, differentiated end to end with JAX.", "description": "Reproduction of Figure 6: QCBM learning a mixture of Gaussians. The QCBM uses 10 qubits and a 5-layer hardware-efficient ansatz. The training objective is to minimize the MMD (Maximum Mean Discrepancy) loss with an Adam optimizer.", "authors": ["Jin-Guo Liu", "Lei Wang"], "contributor": "refraction-ray", "year": 2018, "arxiv_id": "1804.04168", "url": "https://arxiv.org/abs/1804.04168", "tags": ["quantum-machine-learning", "generative-model", "variational-algorithm"], "tc_features": ["circuit", "jit", "vmap", "autodiff"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "4GB"}, "figures": [{"target": "Figure 6", "source": "outputs/result.png", "figure": "figures/2018_qcbm__result.webp", "thumb": "thumbs/2018_qcbm__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2018_qcbm"}, {"slug": "2018_measurement_induced_entanglement", "title": "Measurement-Induced Phase Transitions in the Dynamics of Entanglement", "card_title": "Figure 13(a) · Measurement-induced entanglement", "summary": "Small monitored random circuits show volume-law to area-law entanglement across the measurement-induced transition.", "description": "Reproduces the qualitative content of Figure 13(a) using L=6,8,10,12 qubits and the paper's t=2L unitary layers. Odd and even bonds alternate, and after every layer the two spins on each active bond are subjected to the paper's sequential three-Kraus measurement channel. The original study averages 4000 random-circuit realizations and reaches L=24; this local exact-statevector reproduction uses twelve fixed random circuits, 32 Born-rule trajectories per circuit, and L<=12.", "authors": ["Brian Skinner", "Jonathan Ruhman", "Adam Nahum"], "contributor": "refraction-ray", "year": 2018, "arxiv_id": "1808.05953", "url": "https://arxiv.org/abs/1808.05953", "tags": ["entanglement", "many-body-physics", "random-circuit"], "tc_features": ["circuit", "jit", "vmap"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "4GB"}, "figures": [{"target": "Figure 13(a): von Neumann entropy versus measurement rate", "source": "outputs/result.png", "figure": "figures/2018_measurement_induced_entanglement__result.webp", "thumb": "thumbs/2018_measurement_induced_entanglement__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2018_measurement_induced_entanglement"}, {"slug": "2018_qcnn", "title": "Quantum Convolutional Neural Networks", "card_title": "Figure 2(c) · QCNN phase recognition", "summary": "quimb DMRG ground states feed a TensorCircuit QCNN that separates an SPT phase from the trivial one at N = 11 and N = 45 sites.", "description": "Reproduces the analytical QCNN phase recognition (Figure 2c) using exact ground states obtained from quimb DMRG simulation fed into a TensorCircuit QCNN through quimb2qop. Pauli sums are assembled with PauliStringSum2COO and the contraction is driven by a cotengra contractor.", "authors": ["Iris Cong", "Soonwon Choi", "Mikhail D. Lukin"], "contributor": "refraction-ray", "year": 2018, "arxiv_id": "1810.03787", "url": "https://arxiv.org/abs/1810.03787", "tags": ["quantum-machine-learning", "classification", "topological-phase", "tensor-network"], "tc_features": ["circuit", "jit", "vmap", "contractor", "pauli-operator", "quoperator", "expectation", "interop"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "16GB"}, "figures": [{"target": "Figure 2(c)", "source": "outputs/result.png", "figure": "figures/2018_qcnn__result.webp", "thumb": "thumbs/2018_qcnn__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2018_qcnn"}, {"slug": "2014_qaoa_maxcut", "title": "A Quantum Approximate Optimization Algorithm", "card_title": "Section IV · QAOA on a ring of disagrees", "summary": "TensorCircuit QAOA improves the expected MaxCut ratio on an even ring toward the analytic (2p+1)/(2p+2) curve.", "description": "Reproduces the ring-of-disagrees result from Section IV of the original QAOA paper. The even ring is represented by an exact 12-qubit statevector, and the two angles per layer are optimized by TensorCircuit autodiff with JAX. The original result is an asymptotic statement for n larger than the light cone; p=1,2,3,4 and n=12 are used here so the trend is visible on a laptop.", "authors": ["Edward Farhi", "Jeffrey Goldstone", "Sam Gutmann"], "contributor": "refraction-ray", "year": 2014, "arxiv_id": "1411.4028", "url": "https://arxiv.org/abs/1411.4028", "tags": ["combinatorial-optimization", "quantum-algorithm", "variational-algorithm"], "tc_features": ["circuit", "jit", "autodiff", "expectation"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Section IV: optimized approximation ratio versus QAOA depth", "source": "outputs/result.png", "figure": "figures/2014_qaoa_maxcut__result.webp", "thumb": "thumbs/2014_qaoa_maxcut__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2014_qaoa_maxcut"}, {"slug": "2011_split_step_quantum_walk", "title": "Topological Phenomena in Quantum Walks", "card_title": "Figure 6 · Topological quantum-walk edge state", "summary": "A split-step quantum walk retains a localized interface probability only when the two sides have different winding numbers.", "description": "Reproduces Figure 6 with the paper's parameters theta1=-pi/2, theta2(-infinity)=3pi/4 and two choices of theta2(+infinity). This is a discrete Floquet exact-statevector calculation, so the natural implementation is dense tc.backend matrix-vector evolution with tc.backend.scan and jit rather than a gate-level circuit wrapper. The infinite lattice is truncated to 128 periodic positions and evolved for at most 60 steps, before a boundary can affect the central interface.", "authors": ["Takuya Kitagawa"], "contributor": "refraction-ray", "year": 2011, "arxiv_id": "1112.1882", "url": "https://arxiv.org/abs/1112.1882", "tags": ["topological-phase", "floquet-dynamics", "quantum-algorithm"], "tc_features": ["jit", "scan", "backend-api"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Figure 6: interface-localized versus delocalized probability", "source": "outputs/result.png", "figure": "figures/2011_split_step_quantum_walk__result.webp", "thumb": "thumbs/2011_split_step_quantum_walk__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2011_split_step_quantum_walk"}]</script>
+<script id="gallery-data" type="application/json">[{"slug": "2026_qutrit_time_crystal", "title": "A Qutrit Time Crystal Stabilized with Native Chiral Interactions", "card_title": "Figure 2(b) · Qutrit time-crystal response", "summary": "A driven chiral clock model of 9 qutrits shows period-doubled magnetization and a sharp subharmonic peak in the Fourier spectrum.", "description": "Reproduces Figure 2(b) qualitatively with a noiseless TensorCircuit-NG and JAX simulation of the driven chiral clock model. The original 15-qutrit experiment is scaled to 9 qutrits for fast local execution, while keeping the same Floquet structure U_F = exp(-i H0) exp(-i Hint) X^g, disordered chiral couplings, the spin-1 magnetization observable M = |0><0| - |2><2|, and the DTC-versus-thermal comparison. The microwave kick is modeled as the fractional spectral power of the qutrit shift operator X^g, which is an explicit modeling simplification used to obtain a smooth noiseless interpolation away from the exact g = 1 kick.", "authors": ["Noah Goss", "Nishchay Suri", "Brian Marinelli", "Larry Chen", "Akel Hashim", "Sajant Anand", "Alexis Morvan", "Ravi K. Naik", "Ermal Rrapaj", "David I. Santiago", "Wibe de Jong", "Norman Y. Yao", "Joel E. Moore", "Irfan Siddiqi"], "contributor": "refraction-ray", "year": 2026, "arxiv_id": "2605.14293", "url": "https://arxiv.org/abs/2605.14293", "tags": ["qudit", "floquet-dynamics", "many-body-physics"], "tc_features": ["qudit-circuit", "jit"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Figure 2(b): Single-site magnetization traces and Fourier spectroscopy versus kick strength", "source": "outputs/result.png", "figure": "figures/2026_qutrit_time_crystal__result.webp", "thumb": "thumbs/2026_qutrit_time_crystal__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_qutrit_time_crystal"}, {"slug": "2026_diff_qec_surface", "title": "Differentiable Maximum Likelihood Noise Estimation for Quantum Error Correction", "card_title": "Noise estimation convergence", "summary": "Surface-code noise parameters are recovered by differentiating through a CopyNode tensor-network contraction and optimizing with Adam.", "description": "Reproducing the differentiable maximum likelihood noise estimation for surface code using Tensor Network contraction with CopyNodes. The paper reports no single target figure for this experiment, so the reproduction reports the optimization convergence of the estimated noise parameters.", "authors": ["Hanyan Cao", "Dongyang Feng", "Cheng Ye", "Feng Pan"], "contributor": "refraction-ray", "year": 2026, "arxiv_id": "2602.19722", "url": "https://arxiv.org/abs/2602.19722", "tags": ["quantum-error-correction", "tensor-network"], "tc_features": ["contractor", "jit", "vmap", "autodiff"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "8GB"}, "figures": [{"target": "Maximum-likelihood noise estimation convergence", "source": "outputs/convergence.png", "figure": "figures/2026_diff_qec_surface__convergence.webp", "thumb": "thumbs/2026_diff_qec_surface__convergence.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_diff_qec_surface"}, {"slug": "2026_sat_mps_entanglement", "title": "Entanglement Barriers from Computational Complexity: Matrix-Product-State Approach to Satisfiability", "card_title": "Figure 2 · Entanglement barrier in 3-SAT", "summary": "Imaginary-time propagation of hard 3-SAT instances shows the MPS entanglement entropy peaking near the satisfiability threshold.", "description": "Figure 2 reproduction using the authors' Zenodo protocol (10.5281/zenodo.18743084): Weigt hard-satisfiable 3-SAT generator with p0=0.08, violation-vector Hamiltonian, and continuous tau optimization in [0,7.5] with the same sample-rejection criterion f(7.5) > f(10.0). Scaled down to n=4-15 (Panel A), n=8-10 (Panel B), 200 instances for feasible runtimes while preserving the core physics (linear entropy scaling and alpha_c peak). The bipartite entropy is obtained from a singular value decomposition of the propagated state on the JAX backend rather than from a tc.MPSCircuit.", "authors": ["Tim Pokart", "Frank Pollmann", "Jan Carl Budich"], "contributor": "Qingyun Qian", "year": 2026, "arxiv_id": "2602.20299", "url": "https://arxiv.org/abs/2602.20299", "tags": ["matrix-product-state", "entanglement", "combinatorial-optimization", "tensor-network"], "tc_features": ["backend-api"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "4GB"}, "figures": [{"target": "Figure 2: (a) <S_hat> vs n at alpha_c, (b) <S_hat>/n vs alpha", "source": "outputs/result.png", "figure": "figures/2026_sat_mps_entanglement__result.webp", "thumb": "thumbs/2026_sat_mps_entanglement__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_sat_mps_entanglement"}, {"slug": "2026_quantum_oracle_sketching", "title": "Exponential Quantum Advantage in Processing Massive Classical Data", "card_title": "Figure 4(a) · Machine size versus accuracy", "summary": "Quantum oracle sketching is compared with classical streaming and sparse baselines on an MNIST 3-vs-8 task at matched accuracy.", "description": "Reproduces the Figure 4(a) machine-size versus accuracy trade-off on a binary MNIST task (digits 3 and 8, 2000 samples per class, full 28x28 images reduced by PCA), comparing classical streaming, classical sparse representations, and quantum oracle sketching. A second experiment verifies the sample-complexity theory behind Figure 3(a) by evaluating the expected sketching unitary for a random Boolean oracle on 6 qubits and comparing its operator-norm error against the theoretical O(N/M) bound. That second experiment is diagonal operator algebra written with tc.backend array operations rather than a gate-level tc.Circuit simulation.", "authors": ["Haimeng Zhao", "Alexander Zlokapa", "Hartmut Neven", "Ryan Babbush", "John Preskill", "Jarrod R. McClean", "Hsin-Yuan Huang"], "contributor": "refraction-ray", "year": 2026, "arxiv_id": "2604.07639", "url": "https://arxiv.org/abs/2604.07639", "tags": ["quantum-advantage", "quantum-machine-learning", "classification"], "tc_features": ["backend-api"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Figure 4(a) - Binary classification machine size vs accuracy", "source": "outputs/result.png", "figure": "figures/2026_quantum_oracle_sketching__result.webp", "thumb": "thumbs/2026_quantum_oracle_sketching__result.webp", "script": "main.py"}, {"target": "Figure 3(a) - Boolean oracle sketching error scaling vs O(N/M) bound", "source": "outputs/qos_scaling.png", "figure": "figures/2026_quantum_oracle_sketching__qos_scaling.webp", "thumb": "thumbs/2026_quantum_oracle_sketching__qos_scaling.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2026_quantum_oracle_sketching"}, {"slug": "2026_finite_temperature_lanczos", "title": "Quantum Finite Temperature Lanczos Method", "card_title": "Figure 1(a) · Thermal energy versus temperature", "summary": "Quantum Hutchinson states and a generalized eigenvalue problem give thermal energies of a 10-site TFIM without full diagonalization.", "description": "Reproduces thermal expectation values of energy for the Transverse-Field Ising Model using the Quantum Finite Temperature Lanczos Method (QFTLM). The original system size L=14 is scaled to L=10 for computational feasibility while maintaining the core algorithm logic (Quantum Hutchinson states and generalized eigenvalue problem).", "authors": ["Gian Gentinetta", "Friederike Metz", "William Kirby", "Giuseppe Carleo"], "contributor": "refraction-ray", "year": 2026, "arxiv_id": "2603.25394", "url": "https://arxiv.org/abs/2603.25394", "tags": ["quantum-algorithm", "finite-temperature", "many-body-physics"], "tc_features": ["pauli-operator", "jit", "vmap"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Figure 1(a): Thermal expectation of Energy <E> vs Temperature T", "source": "outputs/result.png", "figure": "figures/2026_finite_temperature_lanczos__result.webp", "thumb": "thumbs/2026_finite_temperature_lanczos__result.webp", "script": "main.py"}], "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", "card_title": "Figure 2(b) · Catastrophic forgetting", "summary": "An 8-qubit amplitude-encoded classifier trained sequentially on MNIST and permuted MNIST forgets the first task as it learns the second.", "description": "This reproduction demonstrates catastrophic forgetting in a quantum classifier by training sequentially on MNIST (0, 9) and permuted MNIST (0, 9). We use an 8-qubit variational quantum circuit with amplitude encoding and 10 layers of hardware-efficient gates, with the layer sweep expressed through tc.backend.scan.", "authors": ["Wenjie Jiang", "Zhide Lu", "Dong-Ling Deng"], "contributor": "refraction-ray", "year": 2021, "arxiv_id": "2108.02786", "url": "https://arxiv.org/abs/2108.02786", "tags": ["quantum-machine-learning", "classification", "variational-algorithm"], "tc_features": ["circuit", "jit", "vmap", "scan", "autodiff", "sampling"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "4GB"}, "figures": [{"target": "Figure 2(b)", "source": "outputs/result.png", "figure": "figures/2021_quantum_continual_learning__result.webp", "thumb": "thumbs/2021_quantum_continual_learning__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2021_quantum_continual_learning"}, {"slug": "2020_efficient_classical_simulation_random_shallow_2d", "title": "Efficient Classical Simulation of Random Shallow 2D Quantum Circuits", "card_title": "SEBD accuracy versus bond dimension", "summary": "Spatial Evolution Block Decimation contracts a random shallow 2D circuit as a PEPS-to-MPS sweep, checked against exact amplitudes.", "description": "This script implements the Spatial Evolution Block Decimation (SEBD) algorithm described in the paper for efficient classical simulation of random shallow 2D quantum circuits. Output amplitudes are compared against exact statevector amplitudes to quantify the truncation error as a function of the MPS bond dimension.", "authors": ["John Napp", "Rolando L. La Placa", "Alexander M. Dalzell", "Fernando G. S. L. Brandão", "Aram W. Harrow"], "contributor": "refraction-ray", "year": 2020, "arxiv_id": "2001.00021", "url": "https://arxiv.org/abs/2001.00021", "tags": ["classical-simulation", "tensor-network", "matrix-product-state", "random-circuit"], "tc_features": ["circuit"], "backend": "numpy", "hardware": {"gpu": false, "min_memory": "8GB"}, "figures": [{"target": "Accuracy comparison plot", "source": "outputs/accuracy.png", "figure": "figures/2020_efficient_classical_simulation_random_shallow_2d__accuracy.webp", "thumb": "thumbs/2020_efficient_classical_simulation_random_shallow_2d__accuracy.webp", "script": "main.py"}], "artifacts": ["outputs/results.log"], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2020_efficient_classical_simulation_random_shallow_2d"}, {"slug": "2019_data_reuploading", "title": "Data Re-uploading for a Universal Quantum Classifier", "card_title": "Figure 6 · Single-qubit universal classifier", "summary": "One qubit re-uploads the input at every layer to act as a universal classifier, trained with L-BFGS on the JAX backend.", "description": "Reproduces the single-qubit classifier experiment (Figure 6) using the data re-uploading technique, with the layer parameters optimized by optax L-BFGS.", "authors": ["Adrián Pérez-Salinas", "Alba Cervera-Lierta", "Elies Gil-Fuster", "José I. Latorre"], "contributor": "refraction-ray", "year": 2019, "arxiv_id": "1907.02085", "url": "https://arxiv.org/abs/1907.02085", "tags": ["quantum-machine-learning", "classification", "variational-algorithm"], "tc_features": ["circuit", "jit", "autodiff", "expectation"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "1GB"}, "figures": [{"target": "Figure 6", "source": "outputs/result.png", "figure": "figures/2019_data_reuploading__result.webp", "thumb": "thumbs/2019_data_reuploading__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2019_data_reuploading"}, {"slug": "2018_qcbm", "title": "Differentiable Learning of Quantum Circuit Born Machine", "card_title": "Figure 6 · QCBM learning a Gaussian mixture", "summary": "A 10-qubit hardware-efficient Born machine trained with an MMD loss to fit a Gaussian mixture, differentiated end to end with JAX.", "description": "Reproduction of Figure 6: QCBM learning a mixture of Gaussians. The QCBM uses 10 qubits and a 5-layer hardware-efficient ansatz. The training objective is to minimize the MMD (Maximum Mean Discrepancy) loss with an Adam optimizer.", "authors": ["Jin-Guo Liu", "Lei Wang"], "contributor": "refraction-ray", "year": 2018, "arxiv_id": "1804.04168", "url": "https://arxiv.org/abs/1804.04168", "tags": ["quantum-machine-learning", "generative-model", "variational-algorithm"], "tc_features": ["circuit", "jit", "vmap", "autodiff"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "4GB"}, "figures": [{"target": "Figure 6", "source": "outputs/result.png", "figure": "figures/2018_qcbm__result.webp", "thumb": "thumbs/2018_qcbm__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2018_qcbm"}, {"slug": "2018_measurement_induced_entanglement", "title": "Measurement-Induced Phase Transitions in the Dynamics of Entanglement", "card_title": "Figure 13(a) · Measurement-induced entanglement", "summary": "Small monitored random circuits show volume-law to area-law entanglement across the measurement-induced transition.", "description": "Reproduces the qualitative content of Figure 13(a) using L=6,8,10,12 qubits and the paper's t=2L unitary layers. Odd and even bonds alternate, and after every layer the two spins on each active bond are subjected to the paper's sequential three-Kraus measurement channel. The original study averages 4000 random-circuit realizations and reaches L=24; this local exact-statevector reproduction uses twelve fixed random circuits, 32 Born-rule trajectories per circuit, and L<=12.", "authors": ["Brian Skinner", "Jonathan Ruhman", "Adam Nahum"], "contributor": "refraction-ray", "year": 2018, "arxiv_id": "1808.05953", "url": "https://arxiv.org/abs/1808.05953", "tags": ["entanglement", "many-body-physics", "random-circuit"], "tc_features": ["circuit", "jit", "vmap"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "4GB"}, "figures": [{"target": "Figure 13(a): von Neumann entropy versus measurement rate", "source": "outputs/result.png", "figure": "figures/2018_measurement_induced_entanglement__result.webp", "thumb": "thumbs/2018_measurement_induced_entanglement__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2018_measurement_induced_entanglement"}, {"slug": "2018_qcnn", "title": "Quantum Convolutional Neural Networks", "card_title": "Figure 2(c) · QCNN phase recognition", "summary": "quimb DMRG ground states feed a TensorCircuit QCNN that separates an SPT phase from the trivial one at N = 11 and N = 45 sites.", "description": "Reproduces the analytical QCNN phase recognition (Figure 2c) using exact ground states obtained from quimb DMRG simulation fed into a TensorCircuit QCNN through quimb2qop. Pauli sums are assembled with PauliStringSum2COO and the contraction is driven by a cotengra contractor.", "authors": ["Iris Cong", "Soonwon Choi", "Mikhail D. Lukin"], "contributor": "refraction-ray", "year": 2018, "arxiv_id": "1810.03787", "url": "https://arxiv.org/abs/1810.03787", "tags": ["quantum-machine-learning", "classification", "topological-phase", "tensor-network"], "tc_features": ["circuit", "jit", "vmap", "contractor", "pauli-operator", "quoperator", "expectation", "interop"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "16GB"}, "figures": [{"target": "Figure 2(c)", "source": "outputs/result.png", "figure": "figures/2018_qcnn__result.webp", "thumb": "thumbs/2018_qcnn__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2018_qcnn"}, {"slug": "2014_qaoa_maxcut", "title": "A Quantum Approximate Optimization Algorithm", "card_title": "Section IV · QAOA on a ring of disagrees", "summary": "TensorCircuit QAOA improves the expected MaxCut ratio on an even ring toward the analytic (2p+1)/(2p+2) curve.", "description": "Reproduces the ring-of-disagrees result from Section IV of the original QAOA paper. The even ring is represented by an exact 12-qubit statevector, and the two angles per layer are optimized by TensorCircuit autodiff with JAX. The original result is an asymptotic statement for n larger than the light cone; p=1,2,3,4 and n=12 are used here so the trend is visible on a laptop.", "authors": ["Edward Farhi", "Jeffrey Goldstone", "Sam Gutmann"], "contributor": "refraction-ray", "year": 2014, "arxiv_id": "1411.4028", "url": "https://arxiv.org/abs/1411.4028", "tags": ["combinatorial-optimization", "quantum-algorithm", "variational-algorithm"], "tc_features": ["circuit", "jit", "autodiff", "expectation"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Section IV: optimized approximation ratio versus QAOA depth", "source": "outputs/result.png", "figure": "figures/2014_qaoa_maxcut__result.webp", "thumb": "thumbs/2014_qaoa_maxcut__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2014_qaoa_maxcut"}, {"slug": "2011_split_step_quantum_walk", "title": "Topological Phenomena in Quantum Walks", "card_title": "Figure 6 · Topological quantum-walk edge state", "summary": "A split-step quantum walk retains a localized interface probability only when the two sides have different winding numbers.", "description": "Reproduces Figure 6 with the paper's parameters theta1=-pi/2, theta2(-infinity)=3pi/4 and two choices of theta2(+infinity). This is a discrete Floquet exact-statevector calculation, so the natural implementation is dense tc.backend matrix-vector evolution with tc.backend.scan and jit rather than a gate-level circuit wrapper. The infinite lattice is truncated to 128 periodic positions and evolved for at most 60 steps, before a boundary can affect the central interface.", "authors": ["Takuya Kitagawa"], "contributor": "refraction-ray", "year": 2011, "arxiv_id": "1112.1882", "url": "https://arxiv.org/abs/1112.1882", "tags": ["topological-phase", "floquet-dynamics", "quantum-algorithm"], "tc_features": ["jit", "scan", "backend-api"], "backend": "jax", "hardware": {"gpu": false, "min_memory": "2GB"}, "figures": [{"target": "Figure 6: interface-localized versus delocalized probability", "source": "outputs/result.png", "figure": "figures/2011_split_step_quantum_walk__result.webp", "thumb": "thumbs/2011_split_step_quantum_walk__result.webp", "script": "main.py"}], "artifacts": [], "code_url": "https://github.com/tensorcircuit/tensorcircuit-ng/tree/master/examples/reproduce_papers/2011_split_step_quantum_walk"}]</script>
 <script>const FEATURES = {"circuit": {"label": "Circuit Simulation", "api": "tc.Circuit"}, "qudit-circuit": {"label": "Qudit Circuit", "api": "tc.QuditCircuit"}, "density-matrix": {"label": "Density Matrix", "api": "tc.DMCircuit"}, "stabilizer": {"label": "Stabilizer Simulation", "api": "tc.StabilizerCircuit"}, "mps-circuit": {"label": "MPS Circuit", "api": "tc.MPSCircuit"}, "analog": {"label": "Analog Evolution", "api": "tc.AnalogCircuit, tc.timeevol"}, "jit": {"label": "JIT", "api": "tc.backend.jit"}, "vmap": {"label": "Vectorization", "api": "tc.backend.vmap"}, "scan": {"label": "Scan", "api": "tc.backend.scan"}, "autodiff": {"label": "Automatic Differentiation", "api": "tc.backend.grad, tc.backend.value_and_grad"}, "contractor": {"label": "Custom Contractor", "api": "tc.set_contractor, tc.contractor"}, "pauli-operator": {"label": "Pauli Operator", "api": "tc.quantum.PauliStringSum2COO, tc.quantum.PauliStringSum2Dense"}, "quoperator": {"label": "QuOperator", "api": "tc.quantum.QuOperator"}, "expectation": {"label": "Expectation", "api": "Circuit.expectation, Circuit.expectation_ps"}, "sampling": {"label": "Sampling", "api": "Circuit.sample"}, "noise": {"label": "Noise Model", "api": "tc.noisemodel, Circuit.unitary_kraus"}, "interop": {"label": "Framework Interop", "api": "tc.quantum.quimb2qop, tc.translation"}, "backend-api": {"label": "Backend API", "api": "tc.backend.* array operations only"}};
 const DATA = JSON.parse(document.getElementById('gallery-data').textContent);
 const BY_SLUG = Object.fromEntries(DATA.map(d => [d.slug, d]));
diff --git a/docs/source/public/reproduce/thumbs/2025_qntk_diagnostics__result.webp b/docs/source/public/reproduce/thumbs/2025_qntk_diagnostics__result.webp
new file mode 100644
index 00000000..8d814833
Binary files /dev/null and b/docs/source/public/reproduce/thumbs/2025_qntk_diagnostics__result.webp differ
diff --git a/examples/reproduce_papers/2025_qntk_diagnostics/main.py b/examples/reproduce_papers/2025_qntk_diagnostics/main.py
new file mode 100644
index 00000000..2151f85e
--- /dev/null
+++ b/examples/reproduce_papers/2025_qntk_diagnostics/main.py
@@ -0,0 +1,465 @@
+"""
+Reproduction of "Towards Practical Quantum Neural Network Diagnostics with Neural Tangent Kernels"
+Link: https://arxiv.org/abs/2503.01966
+
+Description:
+This script reproduces Figure 2 from the paper using TensorCircuit-NG.
+"""
+
+from __future__ import annotations
+
+import argparse
+import contextlib
+import time
+from pathlib import Path
+from typing import Any, Callable, Iterator
+
+from matplotlib import pyplot as plt
+import numpy as np
+import tensorcircuit as tc
+
+plt.switch_backend("Agg")
+
+NQUBITS = 6
+# The paper extends beyond the visible 620-parameter axis; this gallery artifact
+# keeps the six depth points that fit within that plotted range.
+DEPTHS = np.arange(5, 31, 5, dtype=np.int64)
+SEEDS = range(3)
+BACKENDS = ("jax", "pytorch")
+DTYPE = "complex128"
+ENCODING_SCALE = np.pi
+RCOND = 1.0e-10
+ARCHITECTURES = ("low_hva", "high_hva", "low_hea", "high_hea")
+METRICS = ("lambda_min", "inverse_lambda_max", "inverse_condition", "r2")
+
+FIELDS = np.arange(-5.0, 5.0, 0.5, dtype=np.float64)
+SCALED_INPUTS = np.linspace(-0.95, 0.95, FIELDS.size, dtype=np.float64)
+TRAIN_FIELDS = np.array(
+    [-5.0, -3.5, -2.5, -1.0, -0.5, 0.0, 0.5, 1.5, 4.0, 4.5],
+    dtype=np.float64,
+)
+TRAIN_INDICES = np.flatnonzero(np.isin(FIELDS, TRAIN_FIELDS))
+TEST_INDICES = np.flatnonzero(~np.isin(FIELDS, TRAIN_FIELDS))
+
+# The paper does not publish its approximate VQE labels as a table. These
+# values are digitized from the marker centers in the vector datasets figure.
+LABELS = np.array(
+    [
+        -0.823305712,
+        -0.821116171,
+        -0.817501222,
+        -0.813012704,
+        -0.804953841,
+        -0.791620098,
+        -0.767481527,
+        -0.711551981,
+        -0.542529333,
+        -0.258214671,
+        0.002376346,
+        0.256895775,
+        0.549635215,
+        0.711407665,
+        0.767629197,
+        0.792108976,
+        0.804991024,
+        0.812604221,
+        0.817524780,
+        0.820904512,
+    ],
+    dtype=np.float64,
+)
+
+STYLES = {
+    "low_hva": {"color": "#482060", "linestyle": "--", "label": r"low-$\omega$ + HVA"},
+    "high_hva": {"color": "#922b6c", "linestyle": "-", "label": r"high-$\omega$ + HVA"},
+    "low_hea": {"color": "#d84b5f", "linestyle": "--", "label": r"low-$\omega$ + HEA"},
+    "high_hea": {"color": "#ed845b", "linestyle": "-", "label": r"high-$\omega$ + HEA"},
+}
+
+
+def parse_args() -> argparse.Namespace:
+    """Parse the backend used for the reproduction."""
+
+    parser = argparse.ArgumentParser(
+        description="Reproduce Figure 2 with a TensorCircuit-NG backend."
+    )
+    parser.add_argument(
+        "--backend",
+        choices=BACKENDS,
+        default="pytorch",
+        help="Backend for the reproduction (default: pytorch).",
+    )
+    return parser.parse_args()
+
+
+def parameter_count(architecture: str, depth: int) -> int:
+    """Return the trainable parameter count for one circuit."""
+
+    ansatz = architecture.rsplit("_", maxsplit=1)[1]
+    parameters_per_layer = 2 * NQUBITS if ansatz == "hva" else 3 * NQUBITS
+    return parameters_per_layer * depth
+
+
+def initialize_parameters(seed: int, count: int) -> np.ndarray:
+    """Draw one reproducible Uniform(0, 2*pi) initialization."""
+
+    generator = np.random.default_rng(seed)
+    return generator.uniform(0.0, 2.0 * np.pi, size=count).astype(np.float64)
+
+
+def apply_encoding(
+    circuit: tc.Circuit,
+    x_value: Any,
+    depth: int,
+    layer: int,
+    frequency: str,
+) -> None:
+    """Apply the low- or high-frequency data embedding."""
+
+    if frequency == "low":
+        angle = ENCODING_SCALE * x_value / (depth - layer)
+        for qubit in range(NQUBITS):
+            circuit.rx(qubit, theta=angle)
+        return
+    for qubit in range(NQUBITS):
+        circuit.ry(qubit, theta=ENCODING_SCALE * x_value)
+        circuit.rz(qubit, theta=ENCODING_SCALE * x_value * x_value)
+
+
+def apply_cnot_ring(circuit: tc.Circuit) -> None:
+    """Apply the periodic nearest-neighbor CNOT ring."""
+
+    for qubit in range(NQUBITS):
+        circuit.cnot(qubit, (qubit + 1) % NQUBITS)
+
+
+def apply_hva(circuit: tc.Circuit, layer_parameters: Any) -> None:
+    """Apply one Hamiltonian variational ansatz layer."""
+
+    for qubit in range(NQUBITS):
+        circuit.rx(qubit, theta=layer_parameters[0, qubit])
+    for qubit in range(NQUBITS):
+        circuit.rzz(
+            qubit,
+            (qubit + 1) % NQUBITS,
+            theta=layer_parameters[1, qubit],
+        )
+
+
+def apply_hea(circuit: tc.Circuit, layer_parameters: Any) -> None:
+    """Apply one hardware-efficient ansatz layer."""
+
+    rotations = (circuit.rx, circuit.rz, circuit.rx)
+    for sublayer, rotation in enumerate(rotations):
+        for qubit in range(NQUBITS):
+            rotation(qubit, theta=layer_parameters[sublayer, qubit])
+        apply_cnot_ring(circuit)
+
+
+def qnn_output(
+    parameters: Any,
+    x_value: Any,
+    depth: int,
+    architecture: str,
+) -> Any:
+    """Evaluate the representative first-qubit transverse-X expectation."""
+
+    frequency, ansatz = architecture.split("_")
+    ansatz_width = 2 if ansatz == "hva" else 3
+    shaped_parameters = tc.backend.reshape(parameters, [depth, ansatz_width, NQUBITS])
+    circuit = tc.Circuit(NQUBITS)
+    for layer in range(depth):
+        apply_encoding(circuit, x_value, depth, layer, frequency)
+        if ansatz == "hva":
+            apply_hva(circuit, shaped_parameters[layer])
+        else:
+            apply_hea(circuit, shaped_parameters[layer])
+    return tc.backend.real(circuit.expectation_ps(x=[0]))
+
+
+def batch_outputs(
+    parameters: Any,
+    inputs: Any,
+    depth: int,
+    architecture: str,
+) -> Any:
+    """Evaluate a shared-parameter QNN on all scalar inputs."""
+
+    def scalar_output(parameter_values: Any, x_value: Any) -> Any:
+        return qnn_output(parameter_values, x_value, depth, architecture)
+
+    mapped_output = tc.backend.vmap(scalar_output, vectorized_argnums=1)
+    return tc.backend.jit(mapped_output)(parameters, inputs)
+
+
+@contextlib.contextmanager
+def runtime_context(backend: str) -> Iterator[Any]:
+    """Set the selected backend and precision for one complete sweep."""
+
+    with tc.runtime_backend(backend) as active_backend, tc.runtime_dtype(DTYPE):
+        yield active_backend
+
+
+def build_transforms(
+    active_backend: Any, depth: int, architecture: str
+) -> tuple[Callable[[Any, Any], Any], Callable[[Any, Any], Any]]:
+    """Build JIT/vectorized output and Jacobian transforms for one circuit shape."""
+
+    def scalar_output(parameters: Any, x_value: Any) -> Any:
+        return qnn_output(parameters, x_value, depth, architecture)
+
+    output_function = active_backend.jit(
+        active_backend.vmap(scalar_output, vectorized_argnums=1)
+    )
+    if active_backend.name == "pytorch":
+        # TCNG 1.9.1's generic jacrev is incompatible with this PyTorch functorch path.
+        # For this scalar output, grad returns the same parameter Jacobian.
+        scalar_jacobian = active_backend.grad(scalar_output, argnums=0)
+    else:
+        scalar_jacobian = active_backend.jacrev(scalar_output, argnums=0)
+    jacobian_function = active_backend.jit(
+        active_backend.vmap(scalar_jacobian, vectorized_argnums=1)
+    )
+    return output_function, jacobian_function
+
+
+def r2_score(targets: np.ndarray, predictions: np.ndarray) -> float:
+    """Return the coefficient of determination."""
+
+    residual = np.sum(np.square(targets - predictions))
+    total = np.sum(np.square(targets - np.mean(targets)))
+    return float(1.0 - residual / total)
+
+
+def kernel_diagnostics(jacobian: np.ndarray) -> dict[str, float]:
+    """Compute the four diagnostics plotted in Figure 2."""
+
+    train_jacobian = jacobian[TRAIN_INDICES]
+    test_jacobian = jacobian[TEST_INDICES]
+    kernel = train_jacobian @ train_jacobian.T
+    kernel = 0.5 * (kernel + kernel.T)
+    eigenvalues = np.linalg.eigvalsh(kernel)
+    scale = max(float(np.max(np.abs(eigenvalues))), 1.0)
+    if float(eigenvalues[0]) < -1.0e-10 * scale:
+        raise ValueError(f"QNTK is not PSD: minimum eigenvalue {eigenvalues[0]}")
+    eigenvalues = np.where(eigenvalues < 0.0, 0.0, eigenvalues)
+    lambda_min = float(eigenvalues[0])
+    lambda_max = float(eigenvalues[-1])
+    inverse = np.linalg.pinv(kernel, rcond=RCOND, hermitian=True)
+    cross_kernel = test_jacobian @ train_jacobian.T
+    predictions = cross_kernel @ inverse @ LABELS[TRAIN_INDICES]
+    return {
+        "lambda_min": lambda_min,
+        "inverse_lambda_max": 1.0 / lambda_max,
+        "inverse_condition": lambda_min / lambda_max,
+        "r2": r2_score(LABELS[TEST_INDICES], predictions),
+    }
+
+
+def run_sweep(backend: str) -> dict[str, dict[str, np.ndarray]]:
+    """Run all four architectures, six depths, and three initializations."""
+
+    results: dict[str, dict[str, np.ndarray]] = {}
+    with runtime_context(backend) as active_backend:
+        input_tensor = active_backend.convert_to_tensor(SCALED_INPUTS, dtype="float64")
+        transforms: dict[
+            tuple[str, int], tuple[Callable[[Any, Any], Any], Callable[[Any, Any], Any]]
+        ] = {}
+        for architecture in ARCHITECTURES:
+            architecture_metrics = {
+                metric: np.empty((len(SEEDS), DEPTHS.size), dtype=np.float64)
+                for metric in METRICS
+            }
+            for depth_index, depth_value in enumerate(DEPTHS):
+                depth = int(depth_value)
+                transform_key = architecture, depth
+                transforms[transform_key] = build_transforms(
+                    active_backend, depth, architecture
+                )
+                output_function, jacobian_function = transforms[transform_key]
+                count = parameter_count(architecture, depth)
+                for seed in SEEDS:
+                    start = time.perf_counter()
+                    parameters = initialize_parameters(seed, count)
+                    parameter_tensor = active_backend.convert_to_tensor(
+                        parameters, dtype="float64"
+                    )
+                    outputs = output_function(parameter_tensor, input_tensor)
+                    jacobian = jacobian_function(parameter_tensor, input_tensor)
+                    output_values = np.asarray(
+                        active_backend.numpy(outputs), dtype=np.float64
+                    )
+                    if output_values.shape != SCALED_INPUTS.shape:
+                        raise ValueError(
+                            f"Unexpected output shape {output_values.shape}; "
+                            f"expected {SCALED_INPUTS.shape}."
+                        )
+                    diagnostics = kernel_diagnostics(
+                        np.asarray(active_backend.numpy(jacobian), dtype=np.float64)
+                    )
+                    for metric in METRICS:
+                        architecture_metrics[metric][seed, depth_index] = diagnostics[
+                            metric
+                        ]
+                    elapsed = time.perf_counter() - start
+                    print(
+                        f"{architecture}: depth={depth} seed={seed} "
+                        f"R2={diagnostics['r2']:.6f} elapsed={elapsed:.2f}s",
+                        flush=True,
+                    )
+            results[architecture] = architecture_metrics
+    return results
+
+
+def draw_break_marks(top: Any, bottom: Any) -> None:
+    """Draw diagonal marks for a broken vertical axis."""
+
+    diagonal = 0.018
+    style = {"color": "#333333", "clip_on": False, "linewidth": 0.9}
+    top.plot(
+        (-diagonal, diagonal), (-diagonal, diagonal), transform=top.transAxes, **style
+    )
+    top.plot(
+        (1 - diagonal, 1 + diagonal),
+        (-diagonal, diagonal),
+        transform=top.transAxes,
+        **style,
+    )
+    bottom.plot(
+        (-diagonal, diagonal),
+        (1 - diagonal, 1 + diagonal),
+        transform=bottom.transAxes,
+        **style,
+    )
+    bottom.plot(
+        (1 - diagonal, 1 + diagonal),
+        (1 - diagonal, 1 + diagonal),
+        transform=bottom.transAxes,
+        **style,
+    )
+
+
+def plot_results(results: dict[str, dict[str, np.ndarray]]) -> None:
+    """Render the four Figure 2 diagnostics."""
+
+    labels = (
+        r"$\lambda_{\min}$",
+        r"$\lambda_{\max}^{-1}$",
+        r"$\kappa^{-1}$",
+        r"QNTK test $R^2$",
+    )
+    figure = plt.figure(figsize=(16.0, 4.7))
+    grid = figure.add_gridspec(
+        2,
+        4,
+        left=0.065,
+        right=0.99,
+        bottom=0.17,
+        top=0.80,
+        hspace=0.08,
+        wspace=0.35,
+    )
+    axis_a_top = figure.add_subplot(grid[0, 0])
+    axis_a_bottom = figure.add_subplot(grid[1, 0], sharex=axis_a_top)
+    axis_b = figure.add_subplot(grid[:, 1])
+    axis_c_top = figure.add_subplot(grid[0, 2])
+    axis_c_bottom = figure.add_subplot(grid[1, 2], sharex=axis_c_top)
+    axis_d = figure.add_subplot(grid[:, 3])
+    metric_axes = (
+        (axis_a_top, axis_a_bottom),
+        (axis_b,),
+        (axis_c_top, axis_c_bottom),
+        (axis_d,),
+    )
+    for architecture in ARCHITECTURES:
+        style = STYLES[architecture]
+        x_values = np.asarray(
+            [parameter_count(architecture, int(depth)) for depth in DEPTHS]
+        )
+        for axes, metric in zip(metric_axes, METRICS):
+            mean = np.mean(results[architecture][metric], axis=0)
+            standard_deviation = np.std(results[architecture][metric], axis=0)
+            for axis_index, axis in enumerate(axes):
+                axis.plot(
+                    x_values,
+                    mean,
+                    color=style["color"],
+                    linestyle=style["linestyle"],
+                    linewidth=2.2,
+                    marker="o",
+                    markersize=3.4,
+                    label=(
+                        style["label"]
+                        if metric == "lambda_min" and axis_index == 0
+                        else None
+                    ),
+                )
+                axis.fill_between(
+                    x_values,
+                    mean - standard_deviation,
+                    mean + standard_deviation,
+                    color=style["color"],
+                    alpha=0.16,
+                    linewidth=0.0,
+                )
+    top_axes = (axis_a_top, axis_b, axis_c_top, axis_d)
+    for index, (axis, label) in enumerate(zip(top_axes, labels)):
+        axis.set_ylabel(label)
+        axis.text(
+            -0.08,
+            1.05,
+            f"{chr(ord('a') + index)})",
+            transform=axis.transAxes,
+            fontsize=13,
+            fontweight="bold",
+        )
+    all_axes = (
+        axis_a_top,
+        axis_a_bottom,
+        axis_b,
+        axis_c_top,
+        axis_c_bottom,
+        axis_d,
+    )
+    for axis in all_axes:
+        axis.set_xlim(0.0, 620.0)
+        axis.grid(alpha=0.22)
+    for axis in (axis_a_bottom, axis_b, axis_c_bottom, axis_d):
+        axis.set_xlabel("trainable parameters")
+    axis_a_bottom.set_ylim(0.0, 0.5)
+    axis_a_top.set_ylim(0.5, 5.8)
+    axis_b.set_ylim(bottom=0.0)
+    axis_c_bottom.set_ylim(0.0, 0.05)
+    axis_c_top.set_ylim(0.05, 0.72)
+    axis_d.set_ylim(-0.15, 1.08)
+    axis_d.axhline(0.0, color="#555555", linewidth=0.8)
+    for top, bottom in ((axis_a_top, axis_a_bottom), (axis_c_top, axis_c_bottom)):
+        top.spines["bottom"].set_visible(False)
+        bottom.spines["top"].set_visible(False)
+        top.tick_params(labeltop=False, bottom=False, labelbottom=False)
+        bottom.xaxis.tick_bottom()
+        draw_break_marks(top, bottom)
+    figure.legend(
+        *axis_a_top.get_legend_handles_labels(),
+        loc="upper center",
+        bbox_to_anchor=(0.5, 0.98),
+        ncols=4,
+        frameon=False,
+    )
+    output_path = Path(__file__).resolve().parent / "outputs" / "result.png"
+    output_path.parent.mkdir(parents=True, exist_ok=True)
+    figure.savefig(output_path, dpi=180, bbox_inches="tight")
+    plt.close(figure)
+    print(f"saved: {output_path}")
+
+
+def main() -> None:
+    """Configure the backend, run the sweep, and save the figure."""
+
+    args = parse_args()
+    print(f"TensorCircuit backend={args.backend}")
+    plot_results(run_sweep(args.backend))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/reproduce_papers/2025_qntk_diagnostics/meta.yaml b/examples/reproduce_papers/2025_qntk_diagnostics/meta.yaml
new file mode 100644
index 00000000..dafc934e
--- /dev/null
+++ b/examples/reproduce_papers/2025_qntk_diagnostics/meta.yaml
@@ -0,0 +1,30 @@
+title: "Towards Practical Quantum Neural Network Diagnostics with Neural Tangent Kernels"
+arxiv_id: "2503.01966"
+url: "https://arxiv.org/abs/2503.01966"
+year: 2025
+authors:
+  - "Francesco Scala"
+  - "Christa Zoufal"
+  - "Dario Gerace"
+  - "Francesco Tacchino"
+tags:
+  - "quantum-machine-learning"
+  - "variational-algorithm"
+  - "many-body-physics"
+tc_features:
+  - "circuit"
+  - "expectation"
+  - "jit"
+  - "vmap"
+  - "autodiff"
+backend: "pytorch"
+hardware_requirements:
+  gpu: false
+  min_memory: "4GB"
+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."
+outputs:
+  - target: "Figure 2: QNTK spectrum, conditioning, and generalization diagnostics"
+    path: "outputs/result.png"
+    script: "main.py"
diff --git a/examples/reproduce_papers/2025_qntk_diagnostics/outputs/result.png b/examples/reproduce_papers/2025_qntk_diagnostics/outputs/result.png
new file mode 100644
index 00000000..e9ba0371
Binary files /dev/null and b/examples/reproduce_papers/2025_qntk_diagnostics/outputs/result.png differ