论文标题
量子稳定器代码的几何图理论方面
Geometric Graph-Theoretic Aspects of Quantum Stabilizer Codes
论文作者
论文摘要
我们提出了一个系统的程序，用于构建与二进制量子稳定器代码相关的图形。该过程的特征是以下三个步骤过程。首先，稳定器代码被实现为代码稳定（CWS）量子代码。其次，确定了CWS代码的规范形式，第三，输入顶点附加到图形上。为了验证该过程的有效性，我们实施了Gottesman稳定器代码，其特征在于多Qubit的编码运算符，用于对任意单量错误的资源有效误差校正。最后，Gottesman八度量子稳定器代码的错误校正功能以图理论术语验证，如Schlingemann和Werner最初提倡的。
We propose a systematic procedure for the construction of graphs associated with binary quantum stabilizer codes. The procedure is characterized by means of the following three step process. First, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code. Second, the canonical form of the CWS code is determined and third, the input vertices are attached to the graphs. In order to verify the effectiveness of the procedure, we implement the Gottesman stabilizer code characterized by multi-qubit encoding operators for the resource-efficient error correction of arbitrary single-qubit errors. Finally, the error-correcting capabilities of the Gottesman eight-qubit quantum stabilizer code is verified in graph-theoretic terms as originally advocated by Schlingemann and Werner.
