**constructive mathematics**, **realizability**, **computability**

propositions as types, proofs as programs, computational trinitarianism

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 $QBit$ 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 $d = 3$).

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

- 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:

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