nLab qudit




Quantum systems

quantum logic

quantum physics

quantum probability theoryobservables and states

quantum information

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In quantum information theory and quantum computing, by a qdit (or qudit) one means a quantum state in a dd-dimensional Hilbert space, for any natural number dd.

Hence for fixed dd\in \mathbb{N}, the quantum data type of qdits is the dd-dimensional complex vector space equipped with a quantum measurement-basis

dn{1,,d}|n. \mathbb{C}^d \;\simeq\; \underset{n \in \{1, \cdots, d\}}{\bigoplus} \mathbb{C} \cdot \vert n \rangle \,.
  • For d=2d = 2 one speaks of qbits, this is the original terminology;

  • For d=3d = 3 one also speaks of qtrits.


Anyon states

A key example of quantum gates which naturally act on qdits for d>2d \gt 2 are anyon braid-gates in topological quantum computation:

For the potentially realistic case of Chern-Simons theory/WZW-model-controled anyons (such as su(2)-anyons), the elementary quantum logic gates act by the monodromy of the Knizhnik-Zamolodchikov connection on Hilbert spaces of conformal blocks, whose dimension dd is given by a Verlinde formula.

References which make this point explicit include Kolganov, Mironov & Morozov (2023).



See also:

Explicit mentioning of the qdit-nature of the elementary gates in topological quantum computation:

Last revised on November 15, 2023 at 17:37:42. See the history of this page for a list of all contributions to it.