Dissertation for MSc Mathematical and Theoretical Physics at Oxford University

This repo contains the code for my masters' dissertation. The Mathematica notebook notebook.nb grew during the project and was not originally intended to be published; the quality is therefore not en par with coding standards in the Wolfram language. However it might still be useful, so I wanted to make the code available. The quantum simulation software used was QuESTlink/QuEST.

Noisy intermediate-scale quantum (NISQ) computing provides the exciting opportunity of near-term quantum advantage on non-artificial computational problems. Particularly important for the NISQ era are variational quantum algorithms (VQAs), which, for example, allow to approximate the ground state of a quantum Hamiltonian. As noise is a significant cause of concern, realistic noise models are crucial for evaluating such algorithms. A recent and important development in this field is the introduction of Riemannian algorithms with natural gradient [32] and quantum Fisher information (QFI) optimisation [17], which unify and improve upon the performance of previous techniques. I briefly review general aspects of modelling noise in quantum circuits and summarise the relevant theory of VQAs from basic concepts to the recent development of the QFI algorithm. I then present the results of numerical simulations analysing different aspects of the behaviour of this algorithm under noise. In particular, I discuss the influence of hyperparameter choice in situations with noise, a possible performance difference of depolarising and damping noise, the effectiveness of a commonly used initialisation procedure with the optimal computational basis state, the influ- ence of an improved approximation of the continuous time gate/noise dynamics and aspects of a regularisation subprocedure in the algorithm. (citations refer to the references in dissertation.pdf)