Quantum codes, lattices, and CFTs


Dymarsky, A. (2020). Quantum codes, lattices, and CFTs. Perimeter Institute. https://pirsa.org/20110066


Dymarsky, Anatoly. Quantum codes, lattices, and CFTs. Perimeter Institute, Nov. 25, 2020, https://pirsa.org/20110066


          @misc{ pirsa_PIRSA:20110066,
            doi = {10.48660/20110066},
            url = {https://pirsa.org/20110066},
            author = {Dymarsky, Anatoly},
            keywords = {Quantum Fields and Strings, Quantum Information},
            language = {en},
            title = {Quantum codes, lattices, and CFTs},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {nov},
            note = {PIRSA:20110066 see, \url{https://pirsa.org}}

Anatoly Dymarsky Skolkovo Institute of Science and Technology


There is a deep relation between classical error-correcting codes, Euclidean lattices, and chiral 2d CFTs. We show this relation
extends to include quantum codes, Lorentzian lattices, and non-chiral CFTs. The relation to quantum codes provides a simple way to solve
modular bootstrap constraints and identify interesting examples of conformal theories. In particular we construct many examples of physically distinct isospectral theories, examples of "would-be" CFT partition function -- non-holomorphic functions satisfying all constraints of the modular bootstrap, yet not associated with any

known CFT, and find theory with the maximal spectral gap among all Narain CFTs with the central charge c=4. At the level of code theories the problem of finding maximal spectral gap reduces to the problem of finding optimal code, leading to "baby bootstrap" program. We also discuss averaging over the ensemble of all CFTs associated with quantum codes, and its possible holographic interpretation. The talk is based on arXiv:2009.01236 and arXiv:2009.01244.