Quantifying Nonstabilizerness of Codeword-Stabilized Codes
The paper quantifies 'nonstabilizerness' (magic) for codeword-stabilized (CWS) quantum codes, which are candidates for universal quantum computation gates. It shows this magic is determined by the difference structure of the code's classical counterpart, linking it to additive combinatorics. The most magical codes are Sidon sets, and structural analysis reveals that nonstabilizerness remains constant even as the code size grows.