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 (\( {\mathbbm{F}}_{p^m} \) 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.
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Acknowledgments
The work of T. N. was supported in part by the JSPS Grant-in-Aid for Scientific Research (C) No.19K03863, Grant-in-Aid for Scientific Research (A) No. 21H04469, and Grant-in-Aid for Transformative Research Areas (A) “Extreme Universe” No. 21H05182 and No. 21H05190. The research of T. O. was supported in part by Grant-in-Aid for Transformative Research Areas (A) “Extreme Universe” No. 21H05190 and by JST PRESTO Grant Number JPMJPR23F3. The work of K. K. and S. Y. was supported by FoPM, WINGS Program, the University of Tokyo. The work of K. K. was supported by JSPS KAKENHI Grant-in-Aid for JSPS fellows Grant No. 23KJ0436.
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Alam, Y.F., Kawabata, K., Nishioka, T. et al. Narain CFTs from nonbinary stabilizer codes. J. High Energ. Phys. 2023, 127 (2023). https://doi.org/10.1007/JHEP12(2023)127
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DOI: https://doi.org/10.1007/JHEP12(2023)127