nLab qbit (Rev #11)

Context

Computation

Quantum systems

Contents

Idea
Properties
- In terms of geometric quantization
Related concepts
References

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

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

Revision on November 20, 2022 at 10:46:38 by Urs Schreiber See the history of this page for a list of all contributions to it.