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Glossary

Quantum glossary

Bloch sphere

A sphere on which every pure state of a single qubit is one point, and every single-qubit gate is a rotation.

|0⟩ sits at the north pole, |1⟩ at the south, and equal superpositions around the equator, where the longitude is the relative phase. Note that opposite points on the sphere are orthogonal states — the angle on the sphere is twice the angle in the state vector.

|ψ⟩ = cos(θ/2)|0⟩ + e^{iφ} sin(θ/2)|1⟩

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Related terms

  • Qubit — The basic unit of quantum information: a two-level system whose state is a normalised combination of |0⟩ and |1⟩.
  • Phase — The angle of a complex amplitude; relative phases between outcomes decide how they interfere.
  • Pauli gates (X, Y, Z) — The three basic single-qubit operations: X flips the bit, Z flips the phase, Y does both.