基于无消相干子空间的量子避错码设计

针对量子系统的联合消相干模型,可以找到一些不受消相干错误影响的系统状态,这种状态被称为相干保持态,所有相干保持态构成的空间就称为无消相干子空间(decoherencefreesubspace,缩写为DFS).利用DFS的特性可以实现自动容错的量子避错码.首先提出一种DFS的定义,并且以定理的形式证明其他DFS的定义都是等价的.然后给出了DFS的存在性定理.最后利用群论的方法设计一种构造DFS的简单方法 关键词： 相干保持态 无消相干子空间 量子避错码 容错量子计算

Quantum error avoiding code based on the decoherence-free subspace

It has been proved that there exist coherence preserving states which are stable under collective decoherence.Such states are called decoherence free states.All the coherence preserving states constitute a subspace named decoherence free subspace(DFS).DFS can be used to construct quantum error avoiding code which is fault tolerant automatically.We first propose a definition for DFS in this paper,and then prove that nearly all definitions are equivalent.We also prove when there may exist DFS.Finally we show a straightforward way to find the base states of DFS utilizing group theory.