Bloch sphere
The Bloch sphere is the geometric representation of the pure state of a single Qubit as a point on the surface of a unit sphere. Any pure one-qubit state can be written with two angles that fix a direction in three dimensions, so the north and south poles represent the basis states 0 and 1, and every other surface point is a superposition of them.
Use in quantum computing
The Bloch sphere makes single-qubit operations easy to picture. A quantum logic gate acting on one qubit corresponds to a rotation of the sphere about some axis, and a sequence of gates is a sequence of rotations. Points on the surface are pure states; mixed states, which arise from decoherence, sit inside the sphere, with the exact center representing the completely mixed state. The construction, a standard tool in quantum computing, is named after the physicist Felix Bloch.
Sources
- Quantum Computation and Quantum Information (Cambridge University Press, 2010)
- Nuclear Induction (Physical Review 70, 460) (American Physical Society, 1946)
Cite this entry
"Bloch sphere." postquantum.wiki. Updated July 11, 2026. https://postquantum.wiki/bloch-sphere@misc{pqwiki-bloch-sphere,
title = {Bloch sphere},
howpublished = {\url{https://postquantum.wiki/bloch-sphere}},
year = {2026},
note = {postquantum.wiki, updated 2026-07-11}
}