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Paper 1

Qudit surface codes and hypermap codes

Zihan Lei

Year

2021

Journal

arXiv preprint

DOI

arXiv:2112.01752

arXiv

2112.01752

In this article, we define homological quantum codes in arbitrary qudit dimensions $D\geq 2$ by directly defining CSS operators on a 2-Complex $Σ$. If the 2-Complex is constructed from a surface, we obtain a qudit surface code. We then prove that the dimension of the code we define always equals the size of the first homology group of $Σ$. We also define the distance of the codes in this setting, finding that they share similar properties with their qubit counterpart. Additionally, we generalize the hypermap-homology quantum code proposed by Martin Leslie to the qudit case. For every such hypermap code, we construct an abstract 2-Complex whose homological quantum code is equivalent to the hypermap code.

Paper 2

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