nLab qbit

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.

Related concepts

• bit, truth value

• bit flip channel, bit flip code

• quantum logic gate, quantum circuit

• quantum logic, quantum computing, quantum error correction

• dimer

References

The term q-bit goes back to

• Benjamin Schumacher, Quantum coding, Phys. Rev. A 51 (1995) 2738 $[$doi:10.1103/PhysRevA.51.2738$]$

and was popularized by early adoption such as in

• Peter W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52, R2493(R) 1995 (doi:10.1103/PhysRevA.52.R2493)

See also:

• Wikipedia, Qbit

Laboratoy-realizations of qbits for use in quantum computers:

• Qubit Zoo