Anshu, AnuragBreuckmann, Nikolas P.Nirkhe, Chinmay2024-03-182023-06-02Anshu, Anurag, Nikolas P. Breuckmann, and Chinmay Nirkhe. "NLTS Hamiltonians from good quantum codes." In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, pp. 1090-1096. 2023.https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37377983The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the state). We prove this conjecture by showing that the recently discovered families of constant-rate and linear-distance QLDPC codes correspond to NLTS local Hamiltonians.en-USConference Paper2024-03-1810.1145/3564246.3585114