Scaling limits of long-range quantum random walks
R.W.S. Westdorp (TU Delft - Applied Sciences)
F.H.J. REDIG – Mentor
V. V. Dobrovitski – Mentor
J.L.A. Dubbeldam – Graduation committee member
Barbara M. Terhal – Graduation committee member
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Abstract
In this thesis we introduce a variation on the quantum random walk to discuss shifts in an arbitrary range. The concept of Hadamard coin was therefore generalised to a higher order. By a Fourier transform method and a tensor product decomposition of the evolution matrix the long-range quantum random walk was found to converge in distribution to a random variable, different for every range. The limiting random variable consists of three parts: one part fast decaying with the range size, a non-convergent part and a convergent part. Lastly, an introduction was made into the topic of trapped quantum random walks. As a starting point, the survival probability of such a walk on a 3-cycle was calculated and found to scale as 2^(-n), as does the classical trapped random walk on this topology.