# nLab qbit

Contents

### Context

#### Computation

intuitionistic mathematics

# Contents

## Idea

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 $QBit$ is the 2-dimensional complex vector space equipped with its canonical quantum measurement-basis

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

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

## Properties

### 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.

## References

The term q-bit goes back to

and was popularized by early adoption such as in