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Quantum Error Correction Fault Tolerance Topological Quantum Computing

Climbing the Clifford Hierarchy

arXiv
Authors: Luca Bastioni, Samuel Glandon, Tefjol Pllaha, Madison Stewart, Phillip Waitkevich

Year

2026

Paper ID

28392

Status

Preprint

Abstract Read

~2 min

Abstract Words

104

Citations

N/A

Abstract

The Clifford Hierarchy has been a central topic in quantum computation due to its strong connections with fault-tolerant quantum computation, magic state distillation, and more. Nevertheless, only sections of the hierarchy are fully understood, such as diagonal gates and third level gates. The diagonal part of the hierarchy can be climbed by taking square roots and adding controls. Similarly, square roots of Pauli gates (first level) are Clifford gates (climb to the second level). Based on this theme, we study gates whose square roots climb to the next level. In particular, we fully characterize Clifford gates whose square roots climb to the third level.

Why This Paper Matters

  • This paper contributes to the Quantum Error Correction & Fault Tolerance research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • The Clifford Hierarchy has been a central topic in quantum computation due to its strong connections with fault-tolerant quantum computation, magic state distillation, and more.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.12088 [2] arXiv https://arxiv.org/abs/2603.12088 [3] Publisher https://arxiv.org/abs/2603.12088

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