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What is the Bloch sphere?
The Bloch sphere is a geometric picture that shows every state of a single qubit as a point on the surface of a sphere: the north pole is |0⟩, the south pole |1⟩.
A single qubit’s state can be described by two angles: one gives the balance between 0 and 1 (latitude), the other the phase (longitude). Every state therefore corresponds to a point on a sphere. Points on the equator are equal superpositions; their position along the equator shows their phase.
In this picture single-qubit gates rotate the sphere. X swaps the poles, H moves |0⟩ to the equator, and Z, S and T rotate the sphere about the vertical axis by a half, a quarter and an eighth of a turn. The Bloch sphere cannot show entanglement; several qubits need other tools.
Try it yourself
The lesson Phase and the Bloch sphere: the invisible dial lets you try this concept in the browser, with no installation.
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Related concepts
- Qubit · A qubit is the basic unit of information in a quantum computer: measured, it gives 0 or 1, but before measurement it can be in a superposition of both.
- Superposition · Superposition is the quantum state in which a qubit, before it is measured, holds the states 0 and 1 together with definite amplitudes.
- Quantum gate · A quantum gate is a basic operation that reversibly changes the state of one or more qubits; quantum programs are sequences of gates.