量子码哈密顿量低能态的线路下界
量子物理
2022-01-26 v5 计算复杂性
摘要
Freedman与Hastings于2014年提出的无低能平凡态(NLTS)猜想——断言存在一种局域哈密顿量，其所有低能态的复杂度均具有超常数量子线路下界——指出了解决量子PCP猜想的根本障碍。本工作中，我们提供基于熵与局域不可区分性论证的新技术，证明由量子纠错码导出的局域哈密顿量所有低能态的线路下界。对于由近线性码率或近线性距离的LDPC稳定子码导出的局域哈密顿量，我们证明所有能量为o(n)的态均具有超常数线路下界。此类码已知存在，且未必是局部可测试的——而局部可测试性此前被怀疑对NLTS猜想至关重要。有趣的是，此类码也可在二维晶格上构造，表明即使在物理相关系统中，低深度态也无法精确近似基态能量。
引用
@article{arxiv.2011.02044,
title = {Circuit lower bounds for low-energy states of quantum code Hamiltonians},
author = {Anurag Anshu and Chinmay Nirkhe},
journal= {arXiv preprint arXiv:2011.02044},
year = {2022}
}
备注
Previous versions contain revisions to introduction and non-technical content. Prior to version 3, asymptotic constants were worse and the dependency in Theorem 1 was epsilon^{1/3}. Version 5 introduced the lower bound for linear-distance LDPC stabilizer codes which was not in previous versions as well as additional technical appendices