Narain CFTs from nonbinary stabilizer codes
Y. F. Alam, Kohki Kawabata, Tatsuma Nishioka, Takuya Okuda, Shinichiro Yahagi · Journal of High Energy Physics · 2023
Abstract We generalize the construction of Narain conformal field theories (CFTs) from qudit stabilizer codes to the construction from quantum stabilizer codes over the finite field of prime power order ( $$ {\mathbbm{F}}_{p^m} $$ F p m with p prime and m ≥ 1) or over the ring ℤk with k > 1. Our construction results in rational CFTs, which cover a larger set of points in the moduli space of Narain CFTs than the previous one. We also propose a correspondence between a quantum stabilizer code with non-zero logical qubits and a finite set of Narain CFTs. We illustrate the correspondence with well-known stabilizer codes.