NLTS conjecture

In quantum information theory, the no low-energy trivial state (NLTS) conjecture is a lower bound on the complexity of certain classes of quantum states which was conjectured by Michael Freedman and Matthew Hastings in 2013. It was partly intended to be a weaker consequence of a conjectural quantum PCP theorem which would be easier to prove than a full quantum PCP theorem.

A solution to the NLTS conjecture was initially announced in 2015 by Lior Eldar and Aram Harrow, but was modified to prove a weaker statement after a mistake was discovered in the proof. A full proof of the NLTS conjecture given in 2023 by Anurag Anshu, Nikolas Breuckmann, and Chinmay Nirkhe, and was presented at STOC 2023.

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