Diagonal gates in the Clifford hierarchy

Abstract

The Clifford hierarchy is a set of gates that appears in the theory of fault-tolerant quantum computation, but its precise structure remains elusive. We give a complete characterization of the diagonal gates in the Clifford hierarchy for prime-dimensional qudits. They turn out to be $p^m$-th roots of unity raised to polynomial functions of the basis state to which they are applied, and we determine which level of the Clifford hierarchy a given gate sits in based on $m$ and the degree of the polynomial.

8 pages

References in corpus (4)

• Restrictions on Transversal Encoded Quantum Gate Sets
• Qudit versions of the qubit "pi-over-eight" gate
• Maximum nonlocality and minimum uncertainty using magic states
• Order 3 Symmetry in the Clifford Hierarchy

Cited by in corpus (3)

• Climbing the Diagonal Clifford Hierarchy
• Classical Coding Approaches to Quantum Applications
• Quantum Theory from Principles, Quantum Software from Diagrams