论文标题
量子本地可测试的代码持续不断的声音
Quantum Locally Testable Code with Constant Soundness
论文作者
论文摘要
在本文中，我们介绍了具有恒定声音的两个量子可局部测试代码（QLTC）的结构。在第一种方法中，我们介绍了一个称为Check产品的操作，并显示该操作如何引起QLTC的QLTC，持续的声音，恒定速率和距离尺度均与位置相同。在第二种方法中，我们考虑了量子代码和经典重复代码的超图产品，并观察到保留组件代码的声音性的特殊情况。这种洞察力使我们构造了QLTC的QLTC，具有恒定的声音，可扩展率和距离以及恒定的平均位置。我们的工作标志着构建高声音和距离的QLTC迈出的一步，这将为无低能量琐碎状态（NLTS）定理提供不同的结构。
In this paper, we present two constructions of quantum locally testable codes (QLTC) with constant soundness. In the first approach, we introduce an operation called check product, and show how this operation gives rise to QLTCs of constant soundness, constant rate, and distance scaling with locality. In the second approach, we consider hypergraph product of a quantum code and a classical repetition code, and observe a special case in which the soundness of component codes is preserved. This insight leads us to construct QLTCs of constant soundness, scalable rate and distance, and constant average locality. Our work marks a step towards constructing QLTCs of high soundness and distance, which would give a different construction to the No Low-Energy Trivial States (NLTS) theorem.
