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Glossary

Quantum glossary

Amplitude

Also: probability amplitude

The complex number attached to each possible outcome of a quantum state; its squared magnitude is that outcome’s probability.

Amplitudes are not probabilities. They can be negative or complex, which means two paths to the same outcome can cancel each other out — something probabilities can never do. That cancellation is interference, and it is where quantum algorithms get their power.

P(x) = |αₓ|², Σₓ |αₓ|² = 1

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Related terms

  • Born rule — The rule that the probability of a measurement outcome is the squared magnitude of its amplitude.
  • Interference — Amplitudes for the same outcome adding up (constructive) or cancelling (destructive).
  • Phase — The angle of a complex amplitude; relative phases between outcomes decide how they interfere.