ψQMLQUANTUM MACHINE LEARNING
Quantum computing · Statistical learning · Physics-informed intelligence

Quantum meets
machine learning.

A rigorous, visual and practical atlas of quantum machine learning: what the algorithms do, how the mathematics works, where quantum hardware matters, and what the evidence actually supports.

Begin the guided journey ↗Explore all 48 concepts ↗Open interactive lab ↗
$$f_\theta(x)=\langle 0|U^\dagger(x,\theta)\,O\,U(x,\theta)|0\rangle$$
Data → quantum feature map → trainable circuit → measurements → learning
The essential distinction

Quantum learning is not
automatic quantum advantage.

Quantum machine learning explores algorithms that use quantum states, circuits, measurements or quantum data to carry out learning tasks. Some systems are hybrid: classical optimizers update parameters of a quantum circuit. Others use quantum kernels or quantum generative models.

The strongest question is not whether a quantum circuit can fit a dataset. It is whether the full workflow achieves meaningful gains under fair comparisons, realistic access assumptions, and measured hardware costs. The atlas makes those distinctions explicit.

Classical or quantum data→ Feature encoding→ Quantum circuit→ Observable / samples→ Classical loss + optimizer
12 chapters · 48 in-depth concepts

Navigate the discipline.

Chapter 01 · 4 lessonsMathematical & quantum foundationsLinear algebra for QML, Qubits and Bloch sphere, Measurement and expectation values, Entanglement and tensor productsChapter 02 · 4 lessonsClassical ML foundationsSupervised learning and risk, Optimization and gradients, Generalization and model selection, Kernel methods and feature spacesChapter 03 · 4 lessonsData encoding & feature mapsAngle encoding, Amplitude encoding, Basis and computational encoding, Data re-uploading and expressivityChapter 04 · 4 lessonsVariational quantum modelsParameterized quantum circuits, Variational quantum classifier, Quantum neural networks, Parameter-shift gradientsChapter 05 · 4 lessonsQuantum kernels & learning theoryFidelity quantum kernels, Quantum support vector machines, Kernel concentration, Generalization and inductive biasChapter 06 · 4 lessonsOptimization, trainability & noiseBarren plateaus, Local costs and layerwise training, Shot noise and measurement budgets, Hardware noise and error mitigationChapter 07 · 4 lessonsQuantum generative learningBorn machines, Quantum circuit GANs, Quantum autoencoders, Quantum Boltzmann modelsChapter 08 · 4 lessonsQuantum data & scientific MLLearning from quantum states, Quantum state tomography, Quantum phase recognition, Quantum sensing with MLChapter 09 · 4 lessonsReinforcement learning & sequential modelsQuantum reinforcement learning, Quantum policy gradients, Quantum reservoir computing, Time series and quantum recurrent ideasChapter 10 · 4 lessonsAlgorithms, complexity & advantageHHL and quantum linear systems, Quantum PCA and linear algebra, Quantum nearest neighbors, What counts as quantum advantage?Chapter 11 · 4 lessonsApplications & case studiesChemistry and materials, Finance and anomaly detection, Medical and biological signals, Computer vision and hybrid modelsChapter 12 · 4 lessonsResearch practice & deploymentBenchmark design and reproducibility, Software stack and simulation, Cloud architecture and MLOps, Open problems and research roadmap

Interactive intuition.

Explore state preparation, a fidelity kernel, and the trade-off between shot count and statistical precision without installing software.

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