NLTS Hamiltonians from classical LTCs
Quantum Physics
2022-10-11 v2 Computational Complexity
Abstract
We provide a completely self-contained construction of a family of NLTS Hamiltonians [Freedman and Hastings, 2014] based on ideas from [Anshu, Breuckmann, and Nirkhe, 2022], [Cross, He, Natarajan, Szegedy, and Zhu, 2022] and [Eldar and Harrow, 2017]. Crucially, it does not require optimal-parameter quantum LDPC codes and can be built from simple classical LTCs such as the repetition code on an expander graph. Furthermore, it removes the constant-rate requirement from the construction of Anshu, Breuckmann, and Nirkhe.
Cite
@article{arxiv.2210.02999,
title = {NLTS Hamiltonians from classical LTCs},
author = {Zhiyang He and Chinmay Nirkhe},
journal= {arXiv preprint arXiv:2210.02999},
year = {2022}
}
Comments
This note is withdrawn due to an uncorrectable error. A detailed explanation on the withdrawal is hosted on my website at https://nirkhe.github.io/simple_nlts_retraction.pdf