The quantum diamond microscope (QDM) is a device that uses nitrogen-vacancy (NV) color centers in diamond to detect magnetic fields using a technique called optically detected magnetic resonance (ODMR). NV centers are suitable for biological measurements because they can operate at room temperature and diamond is bio-compatible. This thesis works towards integrating this technology in a compact portable quantum bio-sensor, for which a chip with single photon detectors is a promising integration platform. Before this thesis started, a CMOS chip had been fabricated with single photon avalanche diodes (SPAD) on it including circuitry for digital communication.
During this thesis, first, software was improved for an existing confocal ODMR setup, adding all necessary features for 2D scanning routines. Then, a new widefield setup was designed and established for testing the CMOS SPADs. Afterwards, the SPADs were electrically characterized and optically tested, the latter by using the widefield setup. The SPADs dit not function correctly and thus could only be partially characterized, leading to the CMOS design needing to be checked for errors. Finally, an attempt at bio-sensing was made. A sample was prepared by cultivating human embryonic kidney (HEK) cells on diamond, submersed in a 40 $\mu$g/mL solution of magnetic nanoparticles (MNP). During incubation the cells absorbed the MNPs, making them responsive to magnetism. This diamond has been scanned with the confocal setup while applying an external magnetic field of 1.07 mT. No HEK cells were found this way, even though the photo-luminescence intensity map hints at their presence within the scanning area, indicating that the external magnetic field and/or the concentration of the MNPs may be too low. More research is needed to confirm this.

The aim of this thesis was to test the efficiency in practice of an analytical propagator with collision detection for N-body Keplerian systems. This can be used to simulate the evolution of a protoplanetary disk, which gives insight into how planetary systems form. The analytic propagator calculates collisions one by one, while a numerical propagator would compute each time step. The idea of using the analytic propagator is that collisions are rare in astronomical scales, such that jumping from collision to collision and calculating it, is more efficient than calculating all the time steps that are between collisions. Simplifying the orbits of the planetesimals into perfect Keplerian orbits, analytical solutions exist which are used by the analytic propagator.

In this thesis, the runtimes of simulations were measured as well as other properties directly related to the runtime. The overall efficiency of the algorithm with respect to N seemed to be O(N³), which is one power less than previously predicted. The prediction was that the runtime of the full simulation is O(N²ε + N⁴s³/Ia³). Here ε is the maximum eccentricity, s/a is the ratio of a planetesimal's radius to the semi-major axis of its orbit, and I is the maximum inclination. This was calculated by estimating the total number of collisions to be O(N²s²/Ia²) and the runtime for each collision to be O(N²s/a). But the number of collisions turns from quadratic to linear in N, implying that above a certain N almost all planetesimals collide, which reduces the power of N by one. For comparison, the octree code has an algorithmic efficiency of O(N logN) per time step, and the number of steps for a fixed integration time grows as O(N^4/3 log N).