论文标题
组合NLTS的结构
A construction of Combinatorial NLTS
论文作者
论文摘要
NLT（没有低能的琐碎状态）猜想Freedman and Hastings [2014]认为，存在具有高复杂性低的汉密尔顿家族（通过准备状态的量子电路深度衡量的复杂性）。在这里，我们证明了一个称为组合NLTS的较弱版本，其中显示了量子电路下限与违反局部术语的（小）恒定分数的状态。这概括了先前的NETS结果（Eldar和Harrow [2017]； Nirkhe，Vazirani和Yuen [2018]）。我们的构建是通过将张量网络与扩展器代码相结合（Sipser和Spielman [1996]）来获得的。哈密顿量是受扰动张量网络的Hamiltonian，受到Fernandez-Gonzalez et的“哈密顿叔叔”的启发。 al。 [2015]。因此，我们偏离了大多数先前作品中考虑的量子CSS代码哈密顿量。
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 high complexity (with complexity measured by the quantum circuit depth preparing the state). Here, we prove a weaker version called the combinatorial NLTS, where a quantum circuit lower bound is shown against states that violate a (small) constant fraction of local terms. This generalizes the prior NLETS results (Eldar and Harrow [2017]; Nirkhe, Vazirani and Yuen [2018]). Our construction is obtained by combining tensor networks with expander codes (Sipser and Spielman [1996]). The Hamiltonian is the parent Hamiltonian of a perturbed tensor network, inspired by the `uncle Hamiltonian' of Fernandez-Gonzalez et. al. [2015]. Thus, we deviate from the quantum CSS code Hamiltonians considered in most prior works.
