论文标题
低能量子法汉密尔顿的电路下限
Circuit lower bounds for low-energy states of quantum code Hamiltonians
论文作者
论文摘要
Freedman and Hastings的No低能琐碎状态（NLTS），2014年，它提出了当地的哈密顿量的存在，具有超恒定量子电路的下限，基于所有低能量状态的复杂性 - 确定了量子PCP猜想解决方案的基本障碍。在这项工作中，我们基于熵和局部没有可区分的论点提供了新技术，这些论点证明了电路的降低界限，用于由量子误差校正代码引起的所有局部汉密尔顿人的低能状态。 对于由几乎线性速率或几乎线性距离LDPC稳定器代码产生的局部哈密顿量，我们证明了所有能量状态O（n）的复杂性的超稳定电路下限。已知这些代码存在并且不一定是可局部测试的，这是先前怀疑是NLTS猜想所必需的属性。奇怪的是，此类代码也可以在二维晶格上构造，表明低深度状态即使在物理相关的系统中也无法准确近似地面能源。
The No Low-energy Trivial States (NLTS) conjecture of Freedman and Hastings, 2014 -- which posits the existence of a local Hamiltonian with a super-constant quantum circuit lower bound on the complexity of all low-energy states -- identifies a fundamental obstacle to the resolution of the quantum PCP conjecture. In this work, we provide new techniques, based on entropic and local indistinguishability arguments, that prove circuit lower bounds for all the low-energy states of local Hamiltonians arising from quantum error-correcting codes. For local Hamiltonians arising from nearly linear-rate or nearly linear-distance LDPC stabilizer codes, we prove super-constant circuit lower bounds for the complexity of all states of energy o(n). Such codes are known to exist and are not necessarily locally testable, a property previously suspected to be essential for the NLTS conjecture. Curiously, such codes can also be constructed on a two-dimensional lattice, showing that low-depth states cannot accurately approximate the ground-energy even in physically relevant systems.
