Quantum Computation and Simulation with Molecules

理解大量强关联粒子系统的行为是物理学中最重要的开放问题之一。控制复杂的多体现象，如量子磁性和超导性，提供了巨大的潜在应用，但也是一个重大的理论挑战，由于指数大希尔伯特空间。这激发了人们对量子模拟的广泛兴趣，在量子模拟中，一个复杂系统的行为，通常是凝聚态物质，通过一个很好理解的可调系统进行实验建模。量子模拟的最重要的平台是光学晶格中的超冷碱金属原子气体，其中值得注意的亮点包括观察玻色-哈伯德模型的Mott绝缘体和超流相之间的转变。然而，这些原子之间的物理相互作用相对较短，这意味着它们无法模拟具有长程相互作用的系统，其额外的复杂性可能会导致诸如自旋冰和超固体等奇异相。实现可控长程相互作用的平台包括磁性原子，里德伯原子和极性分子。这个博士学位的目的是数值研究实验现实的有限尺寸系统的长程相互作用系统的基态相位，特别关注极性分子。

Understanding the behaviour of systems of large numbers of strongly-correlated particles is oneof the most significant open problems in physics. The control of complex many-body phenomena,such as quantum magnetism and superconductivity, offers great potential applications, but also asignificant theoretical challenge due to the exponentially-large Hilbert space. This has motivatedwide interest in quantum simulation, where the behaviour of a complex system, typically condensedmatter, is experimentally modelled by a well-understood, tunable system. The foremost platformfor quantum simulation has been ultracold alkali atomic gases in optical lattices, with notablehighlights including the observation of the transition between the Mott-insulator and superfluidphases of the Bose-Hubbard model. However, the physical interactions between these atoms arerelatively short-ranged, which means they cannot simulate systems with long-range interactions,whose extra complexity can give rise to exotic phases such as spin ice and supersolidity.Platforms for realising controllable long-range interactions include magnetic atoms, Rydberg atoms,and polar molecules. The aim of this DPhil is to numerically study the ground state phases ofexperimentally realistic finite-size systems of long-range interacting systems, focussing particularlyon polar molecules.