Quantum Machine Learning: a variational circuit that trains itself

This simulation renders a small variational quantum circuit — a row of qubits, each holding a rotation angle θᵢ shown as an arrow on its Bloch sphere, linked by animated entangling gates. Every training step computes the parameter-shift gradient of a toy Hamiltonian's expected energy E(θ) = ⟨ψ(θ)|H|ψ(θ)⟩ and updates θ ← θ − η·∇E(θ), exactly the hybrid quantum-classical loop used by the Variational Quantum Eigensolver (VQE) and by quantum kernel methods in frameworks such as PennyLane and Qiskit Machine Learning.

Watch the energy readout fall and the fidelity readout climb as the circuit converges: qubit count, learning rate, entanglement pattern (linear chain vs. fully connected) and training speed are all adjustable, mirroring the hyperparameters a quantum ML practitioner tunes when designing an ansatz for a real quantum processor.