The effect of measurement uncertainties on quantum random walk based problems
R. den Ouden (TU Delft - Applied Sciences)
J.L.A. Dubbeldam – Mentor (TU Delft - Mathematical Physics)
T. H. Taminiau – Mentor (TU Delft - QID/Taminiau Lab)
Y. M. Blanter – Graduation committee member (TU Delft - QN/Blanter Group)
S.K.J. Aerts – Graduation committee member (TU Delft - Numerical Analysis)
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Abstract
Random walks have been used in a number of different fields for a long time. With the rise of of quantum random walks a lot of these applications have been made more efficient. Recently there have been a lot of improvements in the realization of these quantum random walks in real world systems.
In this research, the effect of uncertainty in the measurement time and measurement frequency are studied on three problems that make use of a quantum random walk. These problems are the network centrality problem, the graph isomorphism problem and the spatial search problem.
These effects are studied by first looking at the theory behind these problems after which the theoretical results of these three problems are calculated. These theoretical results will then be compared to simulated results that have a certain level of uncertainty in the measurement time or frequency.
For both the network centrality problem and the spatial search problem we concluded that only a small error is made when uncertainties are introduced in the system. This implies that these problems are solvable in realizations of the quantum random walk in real world systems. For the Graph isomorphism problem we saw that the error that is made when uncertainties are introduced was large which implies that this problem would only be solvable for small uncertainties.