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"Fault-Tolerant Quantum Computation with Higher-Dimensional Systems", Daniel Gottesman, 1998

Reviewed August 17, 2023

Citation: Gottesman, Daniel. "Fault-tolerant quantum computation with higher-dimensional systems." NASA International Conference on Quantum Computing and Quantum Communications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998.

Web: https://arxiv.org/abs/quant-ph/9802007

Tags: Abelian-anyons, Computer-scientific, Universal-scheme

This is the paper which introduces qudits. Interestingly, the first thing done with qudits was look at error correcting codes on them. These error correcting codes use exactly the Pauli group generalization that naturally arises in TQC. Hence, one can really say that the Zd toric code gives the simplest example of a qudit stabilizer code for every d. Generalized Clifford gates, as well as what gates must be added for universal quantum computing, are also discussed.