Continuous-Time Quantum Walks on Graphs

Vertaalde titel van de scriptie/masterproef: Continuetijd kwantumwandelingen op grafen

Scriptie/Masterproef: Master's Thesis

Samenvatting

The quantum analog of a random walk on a graph is appropriately called a quantum walk on a graph. In these quantum walks, instead of deterministically travelling over the nodes of a graph, we pass through superpositions of the nodes of the graph. Quantum walks are universal for quantum algorithms. Moreover, in the same sense their classical counterparts can exponentially speed up classical computer algorithms, quantum walks have the potential to speed up quantum algorithms exponentially as well. In this thesis, we will study significant properties of these quantum walks on graphs like periodicity, perfect state transfer (PST) and fractional revival (FR). We will do so in the framework of algebraic graph theory.

We describe classifications of several graph properties concerning the so-called continuous quan- tum walks by just using the spectral information of the graphs. Even though there are expressions for periodicity, PST and FR on graphs in terms of its eigenvalues, it remains a difficult task to find (new examples of) graphs allowing the discussed properties. We will therefore pass from general graphs to graphs belonging to association schemes. For these types of graphs there exists a charac- terisation that yields new examples of graphs admitting PST and FR. In this framework, we are able to find large families of graphs on which PST and FR occurs. In particular, the results on association schemes will apply to the well-known distance regular graphs.
Datum prijs30 jun 2022
Originele taalEnglish
Prijsuitreikende instantie
  • Vrije Universiteit Brussel
BegeleiderJan De Beule (Promotor), Sam Adriaensen (Co-promotor) & Sam Mattheus (Co-promotor)

Keywords

  • graph, association scheme, quantum walk

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