Realizing Topological Phases for Quantum Information Processing

本文主要从两个角度对拓扑相的物理可实现性进行理论研究。首先是对几种被提议的哈密顿模型进行数值模拟，这些模型已被提出作为支持非阿贝尔拓扑相的候选模型，其总体目标是：i)确定这些涌现相从物理上现实的哈密顿量产生的条件，ii)表征这些相并分析它们的鲁棒性，以及iii)评估编织操作的效果。第二个是从理论上探索如何利用冷捕获分子来人为地设计一个这样的哈密顿模型。由于紧急现象的数值模拟解决了今天尚未很好理解的新物理学，我们需要新的计算工具来表征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.