English

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This note is withdrawn due to an uncorrectable error.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

R2 v1 2026-06-28T02:56:32.946Z