Quantum Computation and Simulation with Molecules

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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.