nLab qbit




Quantum systems

quantum logic

quantum physics

quantum probability theoryobservables and states

quantum information

quantum computation

quantum algorithms:



In quantum information theory and quantum computing, by a q-bit (or qubit) one means a quantum state in a 2-dimensional complex Hilbert space of states.

Hence the quantum data type QBitQBit is the 2-dimensional complex vector space equipped with its canonical quantum measurement-basis

2|0|1. \mathbb{C}^2 \,\simeq\, \mathbb{C} \cdot \vert 0 \rangle \oplus \mathbb{C} \cdot \vert 1 \rangle \,.

Analogous higher- but still finite- dd-dimensional quantum data (types) are called qdits (“qtrits” for d=3d = 3).


In terms of geometric quantization

In geometric quantization qbits are naturally understood as the states given by the geometric quantization of the 2-sphere for prequantum line bundle (plus metaplectic correction) being of unit first Chern class. See at geometric quantization of the 2-sphere – The space of quantum states.


The term q-bit goes back to

and was popularized by early adoption such as in

See also:

Laboratoy-realizations of qbits for use in quantum computers:

Last revised on November 20, 2022 at 13:07:21. See the history of this page for a list of all contributions to it.