论文标题
从任何古典代码构建量子代码及其在当地哈密顿人的地面上的嵌入
Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians
论文作者
论文摘要
实施健壮的量子误差校正（QEC）对于利用量子技术的承诺是必不可少的。我们引入了一个框架，该框架采用{\ it any}经典代码，并明确构建相应的QEC代码。可以看到我们的框架可以概括CSS代码，并且超越了稳定器形式〜（图〜1）。具体的优势是，经典代码的理想属性自动纳入了生成的量子代码的设计中。我们通过各种插图来衡量理论，其中一些胜过最好的先前结构。然后，我们引入了局部量子自旋链哈密顿量，我们在分析上完全表征其地面空间。我们利用框架证明地面空间包含具有线性距离的显式量子代码。这个侧面置于勇敢的terhal no-go定理。
Implementing robust quantum error correction (QEC) is imperative for harnessing the promise of quantum technologies. We introduce a framework that takes {\it any} classical code and explicitly constructs the corresponding QEC code. Our framework can be seen to generalize the CSS codes, and goes beyond the stabilizer formalism~(Fig.~1). A concrete advantage is that the desirable properties of a classical code are automatically incorporated in the design of the resulting quantum code. We reify the theory by various illustrations some of which outperform the best previous constructions. We then introduce a local quantum spin-chain Hamiltonian whose ground space we analytically completely characterize. We utilize our framework to demonstrate that the ground space contains explicit quantum codes with linear distance. This side-steps the Bravyi-Terhal no-go theorem.
