QuantumCore

QuantumCore

From Hilbert space to quantum machine learning

A rigorous, interactive curriculum paired with an in-browser statevector simulator, circuit builder, Bloch-sphere visualiser and auto-verified labs.

  1. Stage 1

    Mathematical Bedrock & Quantum-Mechanics Axioms

    Complex Hilbert spaces, Dirac notation, Hermitian and unitary operators, the spectral theorem, tensor products, density matrices, partial trace and von Neumann entropy.

  2. Stage 2

    Quantum Information & the Circuit Model

    Qubits and the Bloch sphere, Pauli/Hadamard/phase/rotation gates, CNOT, CZ, SWAP, Toffoli, Bell states, no-cloning, QFT, phase estimation, Grover and HHL.

  3. Stage 3

    Classical-to-Quantum ML Crossover

    Basis, amplitude, angle and Hamiltonian encodings; RKHS and Mercer's theorem; fidelity quantum kernels with SWAP and inversion tests.

  4. Stage 4

    Quantum Machine Learning in the NISQ Era

    Variational circuits, the parameter-shift rule, quantum natural gradient, barren plateaus, noise and error mitigation, QCNN and quantum reservoir computing.