Building manifolds from quantum codes

• Published in: Geometric and functional analysis Vol. 31; no. 4; pp. 855 - 894
• Main Authors: Freedman, Michael, Hastings, Matthew
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.08.2021; Springer Nature B.V
• Subjects: Algorithms; Analysis; Chains; Graph theory; Mathematics; Mathematics and Statistics; Reverse engineering; Riemann manifold

We give a procedure for “reverse engineering" a closed, simply connected, Riemannian manifold with bounded local geometry from a sparse chain complex over Z . Applying this procedure to chain complexes obtained by “lifting" recently developed quantum codes, which correspond to chain comple...