NLTS Hamiltonians from classical LTCs

TL;DR

This paper introduces a new family of NLTS Hamiltonians constructed from simple classical LTCs, avoiding the need for optimal quantum LDPC codes and constant-rate constraints, thus broadening the applicability of NLTS constructions.

Contribution

It provides a self-contained method to build NLTS Hamiltonians from classical LTCs, simplifying previous approaches and removing certain rate constraints.

Findings

Constructs NLTS Hamiltonians from classical LTCs like the repetition code on expanders.

Eliminates the need for optimal-parameter quantum LDPC codes.

Removes the constant-rate requirement from previous NLTS constructions.

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.