NLTM Hamiltonians from gauged sheaf quantum locally testable codes
The work proves a strong version of the No Low-Energy Trivial States conjecture (NLTM) for local Hamiltonians. By constructing frustration-free qubit Hamiltonians using non-Abelian gauged sheaf codes, the authors show that preparing states within a positive energy window from arbitrary stabilizer states requires circuit depths of order Omega(log n). This result excludes classical witnesses based on shallow preparation.