论文标题
有效验证无挫败的汉密尔顿人的基础状态
Efficient Verification of Ground States of Frustration-Free Hamiltonians
论文作者
论文摘要
当地汉密尔顿人的基础状态是多体物理和量子信息处理的关键兴趣。这些状态的有效验证对许多应用至关重要，但非常具有挑战性。在这里，我们提出了一个简单但有力的食谱，用于根据当地的测量来验证一般无挫败的汉密尔顿人的基础状态。此外，我们通过量子可检测性引理（改善）和量子联合结合来得出样品复杂性的严格界限。值得注意的是，当底层哈密顿在本地且陷入困境时，所需的样品数量不会随系统的规模而增加，这是最感兴趣的情况。作为应用程序，我们提出了一种基于局部自旋测量值的任意图上验证Affleck-Kennedy-Lieb-Tasaki（AKLT）状态的一般方法，该方法仅需要在各种晶格上定义的AKLT状态的恒定数量样本。我们的工作不仅对量子信息处理中的许多任务都很感兴趣，而且对多体物理学的研究也很感兴趣。
Ground states of local Hamiltonians are of key interest in many-body physics and also in quantum information processing. Efficient verification of these states are crucial to many applications, but very challenging. Here we propose a simple, but powerful recipe for verifying the ground states of general frustration-free Hamiltonians based on local measurements. Moreover, we derive rigorous bounds on the sample complexity by virtue of the quantum detectability lemma (with improvement) and quantum union bound. Notably, the number of samples required does not increase with the system size when the underlying Hamiltonian is local and gapped, which is the case of most interest. As an application, we propose a general approach for verifying Affleck-Kennedy-Lieb-Tasaki (AKLT) states on arbitrary graphs based on local spin measurements, which requires only a constant number of samples for AKLT states defined on various lattices. Our work is of interest not only to many tasks in quantum information processing, but also to the study of many-body physics.
