We investigate open- and closed-loop quantum optimal control in nitrogen-vacancy (NV) centre systems, using gate set tomography (GST) for pulse characterisation and calibration. Open-loop optimisation with GRAPE revealed a strong dependence of gate fidelity on pulse duration and the need for phase correction in echo-based gates.

Despite promising simulations of advanced pulse designs, experimental performance was consistently higher for a standard weak $\pi$ pulse, highlighting model limitations. Closed-loop optimisation with dCRAB improved performance but exhibited sensitivity to environmental drift, confirming magnet-induced variations.

GST identified dominant coherent error channels, notably ZZ, attributed to AC Stark-induced phase shifts. A novel gate design suppressed ZZ errors but introduced greater stochastic noise.

These results demonstrate the importance of integrating model-driven and data-driven approaches with advanced tomography protocols to achieve robust, high-fidelity quantum control in noisy intermediate-scale quantum (NISQ) devices.

Quantum computing is an emerging field with many promising future applications.
These include, but are not limited to, quantum machine learning, quantum cryptography and quantum chemical engineering.

Before these can be realised, obstacles, which arise due to scaling, need to be overcome.
To accomplish this, quantum processors must be built with low noise and high target gate fidelity rates.
By characterising quantum systems, possible sources of noise can be identified, and consequently, systems can be designed which effectively suppress noise.

Gate Set Tomography (GST) is a protocol developed for the characterisation of quantum processors.
In this research, we apply GST to nitrogen-vacancy (NV) centre systems.
We also construct a widget meant to visualise GST results in an intuitive manner.

Our research is based on twelve models, varying in the number of gates used, the initial state of the nitrogen nucleus, and whether an XY4 echo was applied after gates.
We use simulated and experimental models, and analyse these using the error generator, diamond norm and Nσ metrics.

We conclude that our simulated models capture sources of noise, as the proportion of stochastic errors shifts to Hamiltonian errors when we change our target model from the ideal model to the simulated ones.
We also conclude that the XY4 echo significantly reduces non-Markovianity, which arises due to coupling.
Furthermore, evidence which points to calibration faults is discovered within certain models.
Finally, we present the visualisation widget and show how it can be used to interpret results.