Review of recent progress in constructing codes with transversal non-Clifford gates

          @misc{ pirsa_PIRSA:25040104,
            doi = {10.48660/25040104},
            url = {https://pirsa.org/25040104},
            author = {},
            keywords = {Quantum Information},
            language = {en},
            title = {Review of recent progress in constructing codes with transversal non-Clifford gates},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {apr},
            note = {PIRSA:25040104 see, \url{https://pirsa.org}}
          }
          

Abstract

Quantum codes with transversal non-Clifford gates have many applications in fault tolerant quantum computation, from magic state distillation to robust IQP circuit sampling.

In the past year, there has been spectacular progress on constructing such codes with optimal parameter scaling, i.e., constant encoding rate and constant relative distance.
These constructions rely on quantum versions of algebraic geometry codes, which generalise the well-known Reed-Solomon and Reed-Muller codes. In this talk, we will describe one such construction that yields a family of good codes with a transversal control-control-Z gate, and we will highlight some of the remaining open problems in this area.