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arXiv 1410.0974quant-phcond-mat.str-el
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一维保序拓扑相的基态及其作为量子计算资源态的应用

Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation

Abhishodh Prakash, Tzu-Chieh Wei

摘要:

分类对称保护拓扑(SPT)相在一维的程序最近已经完成,并打开了大门,密切研究属于这些阶段的系统的属性。最近发现,能够基于对称性来约束SPT阶的基态的形式还允许探索用于处理量子信息的新的资源态。在本文中,我们推广了Else等人[Phys. Rev. Lett. { \bf 108},240505(2012)],其中示出了由$\mathbb{Z}_2 \times \mathbb{Z}_2$对称性保护的自旋-1链的基态形式支持身份门的完美操作,这对于量子信息的长距离传输也是重要的。我们开发了一种形式主义来约束任何任意有限对称群保护的SPT相位的基态形式,并使用它来检查由各种有限群保护的SPT相位的基态的例子类似的门保护。我们构造了一个特殊的哈密顿不变量下$A_4$对称变换,这是一个组,允许保护的身份操作,并检查其基态。我们发现存在一个扩展的区域,其中基态是AKLT态,它不仅支持恒等门,而且支持任意的单比特量子门。

英文摘要:

The program of classifying symmetry protected topological (SPT) phases in 1D has been recently completed and has opened the doors to study closely the properties of systems belonging to these phases. It was recently found that being able to constrain the form of ground states of SPT order based on symmetry properties also allows to explore novel resource states for processing of quantum information. In this paper, we generalize the consideration of Else et al. [Phys. Rev. Lett. {\bf 108}, 240505 (2012)] where it was shown that the ground-state form of spin-1 chains protected by $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry supports perfect operation of the identity gate, important also for long-distance transmission of quantum information. We develop a formalism to constrain the ground-state form of SPT phases protected by any arbitrary finite symmetry group and use it to examine examples of ground states of SPT phases protected by various finite groups for similar gate protections. We construct a particular Hamiltonian invariant under $A_4$ symmetry transformation which is one of the groups that allows protected identity operation and examine its ground states. We find that there is an extended region where the ground state is the AKLT state, which not only supports the identity gate but also arbitrary single-qubit gates.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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