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Paper 1

Climbing the Clifford Hierarchy

Luca Bastioni, Samuel Glandon, Tefjol Pllaha, Madison Stewart, Phillip Waitkevich

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.12088

arXiv

2603.12088

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.

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Paper 2

Emergent Heavy-Fermion Physics in a Family of Topological Insulators RAsS (R = Y, La, and Sm).

Robredo I, Fang Y, Chen L, Zaremba N, Prots Y, Krnel M, König M, Iraola MI, Doert T, van den Brink J, Felser C, Si Q, Svanidze E, Vergniory MG

Year

2026

Journal

Journal of the American Chemical Society

DOI

10.1021/jacs.5c21743

arXiv

-

Realizing topological phases in strongly correlated materials has become a major impetus in condensed matter physics. Although many compounds are now classified as topological insulators, -electron systems provide an especially fertile platform for emergent heavy-fermion phenomena driven by the interplay of topology and many-body effects. In this study, we examine the crystalline topology of a new AsS series ( = Y, La, Sm), revealing a structural variant from previous reports. We demonstrate that YAsS and SmAsS host hourglass fermions protected by glide symmetry. SmAsS notably exhibits a strong effective-mass enhancement, placing it alongside SmB and YbB as a material that exemplifies how the Kondo effects pin the correlated -electron states near the Fermi energy and, consequently, renormalize the energy and mass scales of topological surface states without destroying their crystalline protection. This tunability establishes SmAsS as a bridge between weakly correlated topological materials and Kondo insulators. To capture these features, we construct a minimal model incorporating -electron degrees of freedom, which reproduces the observed topological properties and predicts that the surface states survive in the correlated regime, albeit shifted in energy. Our work thus introduces a new family of correlated topological materials and forecasts the robustness of their surface states under Kondo correlations.

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