Transversal Diagonal Logical Operators for Stabiliser Codes

Abstract Storing quantum information in a error correction code can protect it from errors, but the ability to transform stored fault tolerant way is equally important. Logical Pauli group operators be implemented on Calderbank-Shor-Steane (CSS) codes, commonly-studied category of by applying series physical X and Z gates. this form are fault-tolerant because each qubit acted upon at most one gate, limiting spread referred as transversal logical operators. Identifying outside less well understood. first level Clifford hierarchy which deeply connected fault-tolerance universality. In work, we study composed single- multi-qubit diagonal We demonstrate algorithms for identifying all CSS that more general or have lower computational complexity than previous methods. also show method constructing codes desired operator using single phase Our methods rely representing gates XP technique may broader applications.