An ideal characterization of the Clifford operators

What is it about?

It is well-known that the qubit Clifford group is generated by three simple gates: the Phase shift, Hadamard, and CNOT gates. It turns out that, for any finite dimension d, the qudit Clifford group is also generated by the natural generalization of these three gates to higher dimensions. This paper appears to be the first to rigorously (and constructively) prove that these three gates are necessary and sufficient to generate the qudit Clifford group in arbitrary finite dimension.

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Why is it important?

The Clifford group is of fundamental importance to quantum computing. When generalizing to qudit quantum computing, understanding the minimal gate set required for implementing the full set of Clifford operations will be useful in developing universal gate sets and fault-tolerant constructions.