Path Integral Monte Carlo Simulation of Superfluid Ring Lattices

The goal of this work is to lay the groundwork to construct and characterize a quantum device; which we refer to as a superfluid ring lattice; that could serve as a multi-qubit system in the future. Accordingly, a mathematical framework, called the Integer Lattice Method (ILM), is exploited to construct a two-dimensional optical landscape which could facilitate a superfluid ring qubit. The Integer Lattice Method allows one to design and explore both periodic and quasi-periodic structured coherent wave interference patterns. Furthermore, the formalism allows for a direct link to experimental realization. The lattices obtained from ILM can be investigated using WA-PIMC. In particular, the spatial and superfluid density at equilibrium are observables of interest to obtain our objective. In this thesis, the ab-initio Path Integral Monte Carlo Worm algorithm is implemented with the future aim of investigating the construction of superfluid ring lattices. It is written in independent and interchangeable modules in the novel programming language Julia. To ensure scalability, a custom nearest-neighbour algorithm is added. The simulation software is benchmarked by comparing it with exact analytical results from the non-interacting Bose gas model. Emerging issues with our implementation of the Worm algorithm are identified and thoroughly investigated. Finally, some preliminary results on the equilibrium density distribution of the found ILM lattices are presented and discussed.