Results for “Th(CuP)2” | Engineering Papers

DOE OSTI2020

Materials Data on Th(CuP)2 by Materials Project

Th(CuP)2 crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. Th4+ is bonded to six equivalent P3- atoms to form ThP6 octahedra that share corners with twelve equivalent CuP4 tetrahedra, edges with six equivalent ThP6 octahedra, and edges with six equivalent CuP4 tetrahedra. All Th–P bond lengths are 2.90 Å. Cu1+ is bonded to four equivalent P3- atoms to form CuP4 tetrahedra that share corners with six equivalent ThP6 octahedra, corners with six equivalent CuP4 tetrahedra, edges with three equivalent ThP6 octahedra, and edges with three equivalent CuP4 tetrahedra. The corner-sharing octahedra tilt angles range from 22–53°. All Cu–P bond lengths are 2.40 Å. P3- is bonded to three equivalent Th4+ and four equivalent Cu1+ atoms to form a mixture of distorted edge and corner-sharing PTh3Cu4 pentagonal bipyramids.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic States

A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-König bound for $n$-dimensional topological stabilizer codes. In this work, we extend topological Pauli stabilizer codes to a broad class of $n$-dimensional Clifford hierarchy stabilizer codes. These codes correspond to the $(n+1)$D Dijkgraaf-Witten gauge theories with non-Abelian topological order. We construct transversal non-Clifford gates through automorphism symmetries represented by cup products. In 2D, we obtain the first transversal non-Clifford logical gates including T and CS for Clifford stabilizer codes, using the automorphism of the twisted $\mathbb{Z}_2^3$ gauge theory (equivalent to $\mathbb{D}_4$ topological order). We also combine it with the just-in-time decoder to fault-tolerantly prepare the logical T magic state in $O(d)$ rounds via code switching. In 3D, we construct a transversal logical $\sqrt{\text{T}}$ gate in a non-Clifford stabilizer code at the third level of the Clifford hierarchy, located on a tetrahedron corresponding to a twisted $\mathbb{Z}_2^4$ gauge theory. Furthermore, our constructions surpass the Bravyi-König bound by achieving the logical gates in the $(n+1)$-th level of Clifford hierarchy in $n$ spatial dimension.

Kobayashi, Ryohei [Institute for Advanced Study, P↗