Brilliant
Vectors and Matrices
Master vectors, matrices, transformations, and eigenvalues, the essential mathematical foundation for quantum computing, machine learning, and physics.
17 courses · 4 tutorials
Brilliant
Master vectors, matrices, transformations, and eigenvalues, the essential mathematical foundation for quantum computing, machine learning, and physics.
Brilliant
Brilliant's interactive quantum computing course, learn by doing with hands-on puzzles and visualisations. Subscription-based, covered by Brilliant's free trial.
Coursera
SpecialisationPackt
A complete beginner's specialization covering quantum fundamentals, Qiskit programming, and real quantum algorithms, from high-school maths to running code on real quantum hardware.
Coursera
KAIST / Joonwoo Bae
KAIST's beginning-graduate-level introduction to quantum information, taught by Joonwoo Bae. Covers qubits, the axioms of quantum theory, entanglement as a resource, quantum teleportation, gates, circuits, and quantum communication channels.
Coursera
Packt
A hands-on beginner course teaching quantum computing through IBM's Qiskit framework. Starts from quantum mechanics fundamentals and the classical-bit-versus-qubit distinction, then builds up to gates, circuits, the Deutsch-Jozsa algorithm, quantum cryptography, and teleportation.
WOLFRAM LANGUAGE
Wolfram Research
Wolfram's quantum computing framework for Mathematica and the Wolfram Language, offering a unique symbolic computation approach to quantum circuits, ideal for mathematical exploration, visualization, and analysis without writing low-level circuit code.
Coursera
Fractal Analytics (Srinjoy Ganguly, Shalini Devendrababu)
A beginner-friendly introduction to quantum computing from Fractal Analytics. Two modules covering the history and theory of quantum computing, then qubits, superposition, entanglement, quantum gates, and circuits, with hands-on practice in IBM Qiskit.
Udemy
Hoang Quy La
A hands-on Udemy course by Hoang Quy La covering qubits, quantum gates, and quantum circuits in Python with Cirq and Qiskit, plus the Deutsch-Jozsa algorithm, Grover's algorithm, the quantum Fourier transform, quantum phase estimation, variational quantum circuits, and an introduction to quantum error correction.
edX
Delft University of Technology (QuTech)
Learn how quantum information is mathematically represented via quantum circuits and how to manipulate quantum entanglement, a core course in the Quantum 201 program.
IBM Quantum
IBM SkillsBuild
IBM SkillsBuild's free beginner learning content on quantum computing fundamentals. Visual learning activities and virtual labs covering qubits, superposition, entanglement, quantum gates, and basic circuit building.
Microsoft
Microsoft Quantum
Microsoft's free collection of self-paced quantum programming exercises in Q#. Covers quantum basics through advanced algorithms via hands-on kata-style challenges with immediate feedback, runnable in the browser.
IBM Quantum
Dr. Elisa Bäumer and Carmen Recio Valcarce, IBM Quantum
Free two-week Qiskit course on the Hasso Plattner Institute's openHPI platform, taught by IBM Quantum researchers. Covers quantum computing fundamentals, the Qiskit SDK, and implements Deutsch-Jozsa and Grover's algorithm from scratch.
Qiskit
IBM Quantum / Qiskit Team
The original open-source Qiskit Textbook, now archived on GitHub, covering everything from quantum gates and basic circuits to Grover's algorithm, Shor's algorithm, quantum error correction, and quantum machine learning with interactive Jupyter notebooks.
QUBIT
Dr. Donovan
A free, self-paced introduction to quantum computing. Nine modules take you from what a qubit actually is to running your own circuit in Qiskit, using the interactive Bloch sphere and circuit builder throughout. No physics degree required.
QUBITS
Qubit by Qubit instructors (Stanford PhDs)
A two-semester year-long quantum computing course by The Coding School, taught by Stanford PhDs in partnership with Google Quantum AI. Free for partner schools; scholarships available for individual students.
QUANTUM FOURIER TRANSFORM
QWorld volunteer instructors
QWorld's free intermediate quantum programming workshop covering complex numbers, the quantum Fourier transform, and Shor's algorithm. The follow-on to QBronze, run as mentored online sessions through QWorld's global network.
PennyLane
Xanadu
Xanadu's free interactive quantum computing textbook using PennyLane, now hosted as the PennyLane Codebook. Learn quantum computing through coding exercises directly in the browser.
Watch the X, Y and Z gates run on a live Bloch sphere. All three are half-turns around an axis, which explains why X flips a qubit, why Z appears to do nothing, and why applying any of them twice gets you back where you started.
What each quantum gate actually does to a qubit state, with circuit diagrams and matrix forms for Hadamard, Pauli-X/Y/Z, CNOT, Toffoli, and the rotation gates.
Understand quantum gates as 2x2 unitary matrices, see the explicit matrices for X, Y, Z, H, S, and T gates, and learn how matrix multiplication corresponds to running gates sequentially.
The mathematics behind the Bloch sphere: how the angles θ and φ map to quantum state vectors, why single-qubit gates are rotations, and how to read any single-qubit state geometrically.