constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
quantum algorithms:
In quantum information theory and quantum computing, by a qdit (or qudit) one means a quantum state in a $d$-dimensional Hilbert space, for any natural number $d$.
Hence for fixed $d\in \mathbb{N}$, the quantum data type of qdits is the $d$-dimensional complex vector space equipped with a quantum measurement-basis
For $d = 2$ one speaks of qbits, this is the original terminology;
For $d = 3$ one also speaks of qtrits.
A key example of quantum gates which naturally act on qdits for $d \gt 2$ 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 $d$ is given by a Verlinde formula.
References which make this point explicit include Kolganov, Mironov & Morozov (2023).
General:
IEEE Spectrum Qudits: The Real Future of Quantum Computing? (June 2017)
Yuchen Wang, Zixuan Hu, Barry C. Sanders, Sabre Kais, Qudits and High-Dimensional Quantum Computing, Front. Phys. (2020) [doi:10.3389/fphy.2020.589504]
See also:
Explicit mentioning of the qdit-nature of the elementary gates in topological quantum computation:
987 (2023) 116072 [arXiv:2105.03980, doi:10.1016/j.nuclphysb.2023.116072]
Last revised on November 15, 2023 at 17:37:42. See the history of this page for a list of all contributions to it.