# Diagonal gates in the Clifford hierarchy

@article{Cui2017DiagonalGI, title={Diagonal gates in the Clifford hierarchy}, author={S. Cui and D. Gottesman and A. Krishna}, journal={Physical Review A}, year={2017}, volume={95}, pages={012329} }

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… CONTINUE READING

14 Citations

Normal form for single-qutrit Clifford+Toperators and synthesis of single-qutrit gates

- Physics, Mathematics
- 2018

5

ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity

- Mathematics, Physics
- 2018

28

Efficient classical simulation of Clifford circuits with nonstabilizer input states

- Physics, Medicine
- 2019

1

Universal MBQC with generalised parity-phase interactions and Pauli measurements

- Physics, Mathematics
- 2019

4

#### References

##### Publications referenced by this paper.

SHOWING 1-8 OF 8 REFERENCES