Quantum simulation is the notion of experimentally controlling and manipulating physical quantum mechanical resources such that their evolution can be mapped onto a problem that is much harder to solve by any other means. Realising a fully general quantum computer is still a work in progress but we can currently use devices that are purpose built to solve particular classes of problems, so called analogue quantum simulators, to investigate many-body quantum systems. In this thesis we first consider benchmarking the performance of realistic hardware implementations of quantum simulators through simulations of many-body dynamics, where we are able to demonstrate that even with current levels of experimental errors, analogue simulators in ongoing experiments are able to out-perform the best classical algorithms. We next propose how to use these devices in order to study strongly correlated phases induced by interactions in topological band structures, where we place a strong emphasis on how to experimentally realise, prepare and detect these phases for atoms in a Creutz ladder and in a Lieb lattice.We find that in these systems there is an enhanced tendency for interaction induced pairing, allowing for novel pair superfluid phases to be prepared in experiments with ultracold atoms. Finally, we consider additions to these simulators such that they map more closely to many-body systems in realistic solid state settings by including dissipative mechanisms. Specifically, we demonstrate that we are able to classically simulate this behaviour by modifying and hybridising existing numerical methods to allow for the simulation of open many-body systems beyond the Born-Markov approximation. We benchmark this numerical approach by simulating the dynamicsof electrons coupled to a phonon environment, where we find substantial qualitative differences compared to standard open system techniques.
|Date of Award||14 Oct 2020|
- University Of Strathclyde
|Supervisor||Andrew Daley (Supervisor) & Stefan Kuhr (Supervisor)|