Realizing Topological Phases for Quantum Information Processing

该方案主要从两个方面对拓扑相的物理可实现性进行理论研究。第一个是进行数值模拟的几个建议的哈密顿模型，已提出的候选人支持非阿贝尔拓扑相位，与一般目标的i）确定的条件下，这些紧急阶段出现的物理现实的哈密顿，ii）表征这些阶段，并分析其鲁棒性，和iii）评估编织操作的影响。第二个是从理论上探索如何使用冷捕获分子人工设计这样的汉密尔顿模型。由于涌现现象的数值模拟解决了今天还没有很好理解的新物理学，我们需要新的计算工具来描述和理解由此产生的量子多体行为的微妙之处。我们将采用一系列量子蒙特卡罗（QMC）技术来解决这些现象，并根据具体问题的需要引入新的变体。

This proposal focuses on theoretical study of the physical realizability of topological phases from two perspectives. The first is to perform numerical simulations of several proposed Hamiltonian models that have been put forward as candidates for supporting non-Abelian topological phases, with the general goals of i) identifying the conditions under which these emergent phases arise from physically realistic Hamiltonians, ii) characterizing these phases and analyzing their robustness, and iii) evaluating the effects of braiding operations. The second is to explore theoretically how to artificiallyengineer one such Hamiltonian model using cold trapped molecules. Since numerical simulations of emergent phenomena address new physics that is not well understood today, we need new computational tools to characterize and understand the subtleties of the resulting quantum many-body behavior. We shall employ a range of Quantum Monte Carlo (QMC) techniques to address these phenomena, with new variants introduced as required for specific problems.