Scaling limits of long-range quantum random walks

Scaling limits of long-range quantum random walks

Westdorp, Rik (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science)

Redig, F.H.J. (mentor)
Dobrovitski, V.V. (mentor)
Dubbeldam, J.L.A. (graduation committee)
Terhal, B.M. (graduation committee)

Delft University of Technology

Applied Mathematics | Applied Physics

2018-07-27

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.

Quantum
random walk
Probability

http://resolver.tudelft.nl/uuid:c21708c8-dc92-47d9-b0ea-269abce33bd4

Student theses

bachelor thesis

© 2018 Rik Westdorp