Controlled Gates in the Clifford Hierarchy

2024/10/07 by Anderson, Jonas T., Weippert, Matthew · 2 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2410.04711

Abstract

In this note we prove a necessary set of conditions which must be satisfied by any controlled gate in the qubit Clifford Hierarchy. These conditions are straightforward to derive yet quite restricting. We also extend our proofs to gates composed of certain direct sums of unitaries. Finally, we provide some evidence that these conditions are also sufficient.

Cited by

• Characterization of permutation gates in the third level of the Clifford hierarchy
• Affine Equivalence in the Clifford Hierarchy

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• The Clifford hierarchy for one qubit or qudit
• Characterising semi-Clifford gates using algebraic sets
• Permutation gates in the third level of the Clifford hierarchy
• Four qubits generated by Clifford gates
• Five-qubit states generated by Clifford gates