Quantum glossary

Bra-ket notation

Also: dirac notation, ket, bra

Dirac’s notation for quantum states: a ket |ψ⟩ is a column vector, a bra ⟨ψ| its conjugate transpose.

⟨φ|ψ⟩ is an inner product (a number) and |ψ⟩⟨φ| an outer product (a matrix). Once it clicks, most quantum computing papers become readable.

|0⟩ = (1, 0)ᵀ, |1⟩ = (0, 1)ᵀ

See it for yourself

Qubit — The basic unit of quantum information: a two-level system whose state is a normalised combination of |0⟩ and |1⟩.
Amplitude — The complex number attached to each possible outcome of a quantum state; its squared magnitude is that outcome’s probability.