Since their theoretical introduction in 1980, quantum computers have progressed significantly in
both theory and experimentation. Quantum computers have the potential to solve certain prob-
lems significantly faster than their classical counterparts. One particularly promising area is search
algorithms. In 1996, Lov Grover introduced a quantum search algorithm that laid the founda-
tion for numerous variants. Among them, the alternating phase-walk stands out as a method for
searching an element in an ordered list, which is modeled as a graph. However, a major challenge
in practical quantum computing remains quantum decoherence.
The objective of this project was to model decoherence as bond percolation on a star graph
during an alternating phase-walk, and to investigate its resulting effects. The introduction of
decoherence transformed the search algorithm from a deterministic process into a probabilistic
one, as the probability of measuring the marked state is no longer guaranteed to be 100% on every
run of the algorithm. The most significant results were observed when varying the walk time in
the continuous-time quantum walk (CTQW), both with and without a varying initial state. Here,
the optimal time topt and its corresponding maximum average value μmax are presented for each
value of p.
Static Initial State
• N = 3 star graph:
[p = 0.1, topt = 2.46 τ3, μmax = 0.67]
[p = 0.5, topt = 0.62 τ3, μmax = 0.91]
[p = 0.9, topt = 0.37 τ3, μmax = 1.00]
• N = 7 star graph:
[p = 0.1, topt = 2.21 τ7, μmax = 0.56]
[p = 0.5, topt = 0.59 τ7, μmax = 0.96]
[p = 0.9, topt = 0.34 τ7, μmax = 0.99]
• N = 14 star graph:
[p = 0.1, topt = 5.50 τ14, μmax = 0.55]
[p = 0.5, topt = 0.62 τ14, μmax = 0.96]
[p = 0.9, topt = 0.35 τ14, μmax = 0.99]
Varying Initial State
• N = 3 star graph:
[p = 0.1, topt = 2.30 τ3, μmax = 0.68]
[p = 0.5, topt = 0.37 τ3, μmax = 0.70]
[p = 0.9, topt = 0.36 τ3, μmax = 0.99]
• N = 7 star graph:
[p = 0.1, topt = 2.30 τ7, μmax = 0.57]
[p = 0.5, topt = 0.37 τ7, μmax = 0.66]
[p = 0.9, topt = 0.33 τ7, μmax = 0.99]
• N = 14 star graph:
[p = 0.1, topt = 6.42 τ14, μmax = 0.58]
[p = 0.5, topt = 0.39 τ14, μmax = 0.60]
[p = 0.9, topt = 0.34 τ14, μmax = 0.98]

This thesis investigates the peeling-off property of zero rest-mass fields in asymptotically flat space-times, as described by Penrose. Unlike other literature, this work is designed to be accessible to undergraduate physics or mathematics students. It provides a more detailed derivation including numerous explicit calculations, which is appropriate for the assumed background knowledge. The thesis is structured to build from fundamental mathematical concepts to advanced applications in general relativity. The mathematical concepts introduced are topology, compactifications and differential geometry. The main body of the work applies these mathematical tools to the Minkowski space-time and extends the analysis to more general asymptotically flat space-times.

A zero rest-mass field of spin s determines at each event in space-time a set of 2s principal null directions. These are related to the radiative behaviour of the field. These directions exhibit the 'peeling-off' behaviour: to order r^-k-1 (k = 0, ..., 2s), 2s-k directions coincide radially, where r is an affine parameter on a null geodesic. Criteria for asymptotically simple and asymptotically flat space-times are given, and this peeling-off behaviour is studied in these settings. This involves the introduction of points 'at infinity' through a conformal completion. These points at infinity then become an ordinary hypersurface ℑ to the conformally completed manifold. The conformal transformations of zero rest-mass fields are investigated so that their behaviour at infinity can be studied at this hypersurface. If the transformed field is continuous at ℑ, we find that the peeling-off property holds. If the Einstein empty-space equations without cosmological constant hold near the boundary, the transformed gravitational field is found to be continuous at the boundary, so that the peeling-off property holds.

This thesis is on characterizing the superconducting properties of NbTiN thin films under cryogenic conditions for potential applications in modular quantum computers. The characterization involves development of a measurement setup using a four-point probe method, which measures resistivityof magnetron sputtered thin films of NbTiN at room temperature and (cryogenic) temperature near ab- solute zero.
The results revealed unexpected resistivity values at 3.3 K, questioning the sample’s elemental com- position. Despite superconductivity not being reached by the setup, the research shows how impor- tant optimal elemental composition is and that the implementation of pulsed currents minimizes Joule Heating.
Despite not having characterized superconducting properties, taking steps back might be essential to take a step forward in developing a quantum computer.
This thesis was carried out at TU Delft as part of the Bachelor Final Project course.