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

  1. Quantum Computation and Quantum Information (Cambridge University Press, 2010)
  2. 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} }