通过模拟量子二聚体模型设计拓扑保护量子计算的奇异相位
Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models
摘要：
我们使用非微扰扩展承包商重整化（ENCORE）方法工程量子器件的拓扑保护的量子位的实现所描述的一个有效的量子二聚体模型的三角晶格。通过调整设备的耦合，拓扑保护可能会实现，如果有效的两个二聚体之间的相互作用和翻转幅度的比率在于在液相的量子二聚体模型的相图。基于量子约瑟夫森结阵列的方案[L. B. Ioffe { \it等人}，Nature（London）{ \bf 415}，503（2002）]我们的结果表明，只有在包括标准量子二聚体模型中不存在的并且涉及三个或四个二聚体的额外相互作用和二聚体翻转的情况下，才能获得低于1 mK的最佳操作温度。目前还不清楚量子二聚体哈密顿量中的这些额外项是否破坏了量子计算所需的液相。使多二聚体项的影响最小化将需要纳米开尔文区域中的能量尺度。一个替代的实现基于冷原子或分子气体加载到光晶格也进行了讨论，它表明，所涉及的小能量尺度-意味着长的操作时间-使这样的设备不切实际。考虑到设备中裸耦合之间的数量级以及拓扑间隙，在量子设备中实现拓扑相需要仔细的工程和大的裸相互作用尺度。
英文摘要：
We use a nonperturbative extended contractor renormalization (ENCORE) method for engineering quantum devices for the implementation of topologically protected quantum bits described by an effective quantum dimer model on the triangular lattice. By tuning the couplings of the device, topological protection might be achieved if the ratio between effective two-dimer interactions and flip amplitudes lies in the liquid phase of the phase diagram of the quantum dimer model. For a proposal based on a quantum Josephson junction array [L. B. Ioffe {\it et al.}, Nature (London) {\bf 415}, 503 (2002)] our results show that optimal operational temperatures below 1 mK can only be obtained if extra interactions and dimer flips, which are not present in the standard quantum dimer model and involve three or four dimers, are included. It is unclear if these extra terms in the quantum dimer Hamiltonian destroy the liquid phase needed for quantum computation. Minimizing the effects of multi-dimer terms would require energy scales in the nano-Kelvin regime. An alternative implementation based on cold atomic or molecular gases loaded into optical lattices is also discussed, and it is shown that the small energy scales involved--implying long operational times--make such a device impractical. Given the many orders of magnitude between bare couplings in devices, and the topological gap, the realization of topological phases in quantum devices requires careful engineering and large bare interaction scales.
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