论文标题
有效验证Affleck-Kennedy-Lieb-Tasaki州
Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
论文作者
论文摘要
Affleck-Kennedy-Lieb-Tasaki（AKLT）状态是一类重要的多体量子状态，在量子信息处理中有用，包括基于测量的量子计算。在这里，我们提出了一种用局部自旋测量的任意图上的AKLT状态构建有效验证协议的通用方法。我们的验证协议建立在债券验证协议和基础图的匹配封面（包括边缘着色）上，这些图形具有简单的几何图像和图形图。我们还提供了严格的性能保证，这是实际应用所需的。通过我们的方法，可以以恒定的样本成本来验证大多数具有广泛关注的AKLT状态，包括在1D和2D晶格上定义的状态，该态度与系统大小无关，并且比所有以前的方法都更有效。作为例证，我们在各种晶格和多达五个顶点上为AKLT状态构建了AKLT状态的具体验证协议。
Affleck-Kennedy-Lieb-Tasaki (AKLT) states are an important class of many-body quantum states that are useful in quantum information processing, including measurement-based quantum computation in particular. Here we propose a general approach for constructing efficient verification protocols for AKLT states on arbitrary graphs with local spin measurements. Our verification protocols build on bond verification protocols and matching covers (including edge coloring) of the underlying graphs, which have a simple geometric and graphic picture. We also provide rigorous performance guarantee that is required for practical applications. With our approach, most AKLT states of wide interest, including those defined on 1D and 2D lattices, can be verified with a constant sample cost, which is independent of the system size and is dramatically more efficient than all previous approaches. As an illustration, we construct concrete verification protocols for AKLT states on various lattices and on arbitrary graphs up to five vertices.
