With the rapid development of Quantum Computers (QC) and QC Simulators, there will be an increased demand for functioning Quantum Algorithms in the near future. Some of the most ubiquitously useful algorithms are solvers for linear systems of equations. Since the conception of the Quantum Linear Solver Algorithm (QLSA) by Harrow, Hassidim and Lloyd (HHL) in 2009, many improvements have been made, although a generic implementation for arbitrary matrices and vectors is still not available. In this thesis a variant of the HHL QLSA is studied, and the open challenges are investigated. Solutions for two of the challenges, namely the Eigenvalue Inversion subroutine and the Higher-Order Ancilla Rotation subroutine, are discussed. As part of the thesis project, these subroutines have been implemented in the QX Quantum Computer Simulator, and the subroutines are combined to form a complete Quantum Linear Solver (QLS), with the restraint that the implementation for the vector and Hamiltonian of the matrix must be provided by the user. A proof-of-concept QLS by Cao et al. is also implemented in the QX simulator, and using the implementation of the vector and Hamiltonian of Cao et al. the complete solver is tested. In the process of this thesis, a framework for basic Quantum Arithmetic is built providing three variants of Integer Adders, two variants of Integer Subtracters, one Integer Multiplier and one Integer Divider. In addition, gates not natively available in the QX simulator are implemented, and a number of improvements and extensions of algorithms presented in the literature are given, making the described algorithms function on the QX simulator and extending features.

Crucial to the behaviour of a Nitrogen-Vacancy (NV) centre are its excited state cyclicities, determining the ability to perform high fidelity readout, spin-photon entanglement generation or fast spinpumping. This work presents a unified model to predict these excited state cyclicities over a wide range of strain, electric field, magnetic field and temperature, a useful tool for a model based predictive engineering approach towards the development of new NV qubits. A set of measurements was performed to verify the prediction made by the model and improve the model over a wide range of perpendicular strain up to 7.5 GHz. An automated photon detection efficiency measurement was implemented, showing an average PSB photon detection efficiency of 2.8(3)% in the given setup. The cyclicities of the |Ex⟩ and |Ey⟩ excited states were measured over the given strain range for a single NV centre, showing a severe drop in cyclicity towards higher strain for both transition, a convergence of cyclicities towards zero strain, and a consistently higher cyclicity for |Ex⟩ compared to |Ey⟩, as predicted by the model. However, clear differences were discovered between predictions and measurements, with the recommendation to repeat the measurement at a lower sample temperature of 4K where temperature mixing is negligible. A framework was developed to measure the excited state branching ratios into and out of the singlet states, and were measured for the |E1,2⟩ states, showing that significant singlet branching remains present at high strain. However, a broken optical device prevented accurate measurements. Furthermore, an optimisation framework was developed, implemented and verified for a mirror coupling light out of a quantum frequency converter into a telecom fibre; one of the final steps towards an operationally autonomous NV quantum network node.