论文标题
利用堕落来构建良好的三元量子错误纠正代码
Exploiting degeneracy to construct good ternary quantum error correcting code
论文作者
论文摘要
通常，可以直接从量子系统的代码构建更高维系统的量子错误校正代码。尚不清楚的是，是否存在针对更高维系统的有效代码设计技术。在本文中，我们为三元量子系统提出了一个7 Qutrit错误校正代码，并表明该设计配方在量子系统中没有等效性。该代码在维护CSS结构时纠正单个错误所需的QUTRIT数量是最佳的。该退化的CSS代码可以（i）可以（i）纠正多达七个同时的相错误和一个位错误，（ii）在二十一对中的十分之一的Qutrit上正确纠正两个同时的位错误，而（iii）在实施成本中，该法规仅是两个更高的代码。我们提出的代码表明，可以针对三元量子系统明确设计更好的代码，而不是简单地使用二进制量子系统的代码。
Quantum error-correcting code for higher dimensional systems can, in general, be directly constructed from the codes for qubit systems. What remains unknown is whether there exist efficient code design techniques for higher dimensional systems. In this paper, we propose a 7-qutrit error-correcting code for the ternary quantum system and show that this design formulation has no equivalence in qubit systems. This code is optimum in the number of qutrits required to correct a single error while maintaining the CSS structure. This degenerate CSS code can (i) correct up to seven simultaneous phase errors and a single bit error, (ii) correct two simultaneous bit errors on pre-defined pairs of qutrits on eighteen out of twenty-one possible pairs, and (iii) in terms of the cost of implementation, the depth of the circuit of this code is only two more than that of the ternary Steane code. Our proposed code shows that it is possible to design better codes explicitly for ternary quantum systems instead of simply carrying over codes from binary quantum systems.
