NLTS Hamiltonians from good quantum codes
Quantum Physics
2024-12-06 v4 Statistical Mechanics
Computational Complexity
Abstract
The 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.
Cite
@article{arxiv.2206.13228,
title = {NLTS Hamiltonians from good quantum codes},
author = {Anurag Anshu and Nikolas P. Breuckmann and Chinmay Nirkhe},
journal= {arXiv preprint arXiv:2206.13228},
year = {2024}
}
Comments
12 pages, 1 figure, both updated versions update funding information and clarify discussions. No technical content changed between versions