Nikolas Breuckmann

The NLTS Theorem: Constructing a fully quantum universe using error correcting codes, complexity theory and expansion

The no low-energy trivial states (NLTS) conjecture posits that, loosely speaking, there exists a physical system that below a certain energy cannot be approximated by a classical ansatz. This conjecture was formulated in 2013 by Fields Medalist Michael Friedman and Matt Hastings at Microsoft Research.

We will discuss the resolution of this conjecture [Anshu, NPB, Nirkhe 2022], which relies on the construction of certain error correcting codes that were developed to make quantum computers robust against the debilitating effects of noise. We will highlight the geometric ideas behind the construction and, in particular, discuss the role of expansion in higher dimensional systems and a clustering property of approximations of homological cycles.

In our observable universe, quantum effects manifest prominently only in microscopic systems and they become irrelevant once we transition to scales relevant to human experience. However, in the hypothetical world constructed from error-correcting codes where the NLTS Theorem holds, a non-Newtonian behaviour prevails across all scales. This result also gives a rigorous proof of the stability of quantum effects at non-zero temperature, and is a step towards proving the quantum PCP conjecture, considered the most important open problem in quantum information theory.