Laboratoire de Physique Théorique et Hautes Énergies, CNRS UMR 7589 et Université Paris 6, Boîte 126, 4 place Jussieu, 75252 Paris Cedex 05, France.
Rep Prog Phys. 2012 Jul;75(7):072001. doi: 10.1088/0034-4885/75/7/072001. Epub 2012 Jun 28.
We review the general notion of topological protection of quantum states in spin models and its relation with the ideas of quantum error correction. We show that topological protection can be viewed as a Hamiltonian realization of error correction: for a quantum code for which the minimal number of errors that remain undetected is N, the corresponding Hamiltonian model of the effects of the environment noise appears only in the Nth order of the perturbation theory.We discuss the simplest model Hamiltonians that realize topological protection and their implementation in superconducting arrays. We focus on two dual realizations: in one the protected state is stored in the parity of the Cooper pair number, in the other, in the parity of the flux number. In both cases the superconducting arrays allow a number of fault-tolerant operations that should make the universal quantum computation possible.
我们回顾了自旋模型中量子态的拓扑保护的一般概念及其与量子纠错思想的关系。我们表明，拓扑保护可以看作是错误校正的哈密顿实现：对于一个量子码，其中未被检测到的最小错误数为 N，则环境噪声影响的相应哈密顿模型仅出现在微扰理论的第 N 阶。我们讨论了实现拓扑保护的最简单模型哈密顿，并讨论了它们在超导阵列中的实现。我们重点讨论了两种对偶实现：在一种实现中，受保护的状态存储在 Cooper 对数量的奇偶校验中，在另一种实现中，存储在通量数量的奇偶校验中。在这两种情况下，超导阵列都允许进行一些容错操作，这应该使通用量子计算成为可能。
