Crash Course

Learn about quantum computing.

These pages are arranged by what they build on, not by any order you have to follow. Each one lists what to read first, so you can start at the top or jump straight to a topic and work backwards from there.

Start here · no prerequisites

Linear Algebra BasicsThe vectors, matrices, and inner products that quantum computing is built on.SourcesRecommended books, courses, and references for learning quantum computing.
Bra-Ket NotationThe notation used to write quantum states, and the operations that go with it.RequiresLinear Algebra BasicsMotivation, Qubits, Bloch SphereWhy quantum computing matters, what a qubit is, and how to picture one.RequiresLinear Algebra Basics
Superposition, Single-Qubit Gates, Intro to QiskitA formal definition of superposition, the single-qubit gates, and your first circuit in Qiskit.RequiresMotivation, Qubits, Bloch Sphere · Bra-Ket Notation
Controlled Gates, Entanglement, Bell StatesTwo-qubit gates, entanglement, and the four Bell states.RequiresSuperposition, Single-Qubit Gates, Intro to QiskitUsing Quantum HardwareHow to run the circuits you build on a real quantum backend.RequiresSuperposition, Single-Qubit Gates, Intro to Qiskit
Deutsch-Jozsa, Simon's AlgorithmsThe first algorithms that beat every possible classical approach.RequiresControlled Gates, Entanglement, Bell StatesPseudo-Telepathy, Superdense Coding, TeleportationProtocols that use entanglement to do things classical communication cannot.RequiresControlled Gates, Entanglement, Bell StatesToffoli Gate, UniversalityThree-qubit gates and what it means for a gate set to be universal.RequiresControlled Gates, Entanglement, Bell States
Bernstein-Vazirani Algorithm, Intro to ClassiqAnother oracular algorithm, and a higher-level way to describe quantum circuits.RequiresDeutsch-Jozsa, Simon's AlgorithmsCHSH GameA game that quantum strategies win more often than any classical strategy can.RequiresPseudo-Telepathy, Superdense Coding, TeleportationGrover's AlgorithmSearching an unstructured space quadratically faster than any classical search.RequiresDeutsch-Jozsa, Simon's Algorithms
Quantum Fourier Transform, Phase EstimationThe transform and the estimation routine that most advanced algorithms are built from.RequiresGrover's AlgorithmRotation Matrices, Amplitude AmplificationThe geometry underneath Grover's algorithm, generalized.RequiresGrover's Algorithm
Iterative Quantum Phase EstimationPhase estimation rewritten to use far fewer qubits.RequiresQuantum Fourier Transform, Phase EstimationShor's AlgorithmFactoring large integers efficiently, and what that means for encryption.RequiresQuantum Fourier Transform, Phase EstimationVariational Quantum EigensolverFinding the minimum eigenvalue of a Hamiltonian with a hybrid algorithm.RequiresQuantum Fourier Transform, Phase Estimation
Quantum Key Distribution, BB84 ProtocolUsing quantum mechanics to share a key that cannot be intercepted unnoticed.RequiresShor's Algorithm
Post-Quantum Cryptography, KyberClassical encryption schemes believed to resist quantum attack.RequiresQuantum Key Distribution, BB84 Protocol