Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice
Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice
复制标题
三维晶格上的局部非Calderbank-Shor-Steane量子纠错码
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Isaac H. Kim
中科院分区：
文献类型：
--
作者：
Isaac H. Kim
我们提出了一个非钙库 - steane量子误差校正代码的家族，该代码由3D晶格上的几何局部稳定器发电机组成。我们研究了由局部稳定器发生器集合集的铁磁相互作用构建的哈密顿量。系统的退化基态的特征是量子误差校正代码，其编码量子的数量等于歧管的第二个贝蒂数。这些模型（i）仅具有局部相互作用； （ii）在双重晶格上承认与伊辛模型具有强烈的二元性关系； （iii）在基态下具有拓扑顺序，其中一些在有限温度下存活； （iv）在有限温度下作为经典记忆行为。
We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.