10 min•Beginner
Quantum states
We write qubit states with 'ket' notation: |0⟩ and |1⟩. A general state mixes them with complex numbers called amplitudes.
Learning objectives
- Read the notation |0⟩ and |1⟩.
- Understand amplitudes and probabilities.
Ket notation
|0⟩ and |1⟩ are the two basis states. A qubit state |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex amplitudes.
Probabilities
The probability of measuring 0 is |α|², and of measuring 1 is |β|². They must sum to 1.
Key terms
Amplitude
A complex number attached to a basis state.
Ket
The notation |x⟩ for a quantum state.
Checkpoint
If |ψ⟩ = (1/√2)|0⟩ + (1/√2)|1⟩, what is the probability of measuring 0?