Quantum Computation and Simulation with Molecules

Understanding the behaviour of systems of large numbers of strongly-correlated particles is one
of 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 a
significant theoretical challenge due to the exponentially-large Hilbert space. This has motivated
wide interest in quantum simulation, where the behaviour of a complex system, typically condensed
matter, is experimentally modelled by a well-understood, tunable system. The foremost platform
for quantum simulation has been ultracold alkali atomic gases in optical lattices, with notable
highlights including the observation of the transition between the Mott-insulator and superfluid
phases of the Bose-Hubbard model. However, the physical interactions between these atoms are
relatively 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 of
experimentally realistic finite-size systems of long-range interacting systems, focussing particularly
on polar molecules.