English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Quantum walks exhibit properties without classical analogues. One of those isthe phenomenon of asymptotic trapping -- there can be non-zero probability ofthe quantum walker being localised in a finite part of the underlying graphindefinitely even though locally all directions of movement are assignednon-zero amplitudes at each step. We study quantum walks with the flip-flopshift operator and the Grover coin, where this effect has been identifiedpreviously. For the version of the walk further modified by a random dynamicaldisruption of the graph (percolated quantum walks) we provide a recipe for theconstruction of a complete basis of the subspace of trapped states allowing todetermine the asymptotic probability of trapping for arbitrary finite connectedsimple graphs, thus significantly generalizing the previously known resultrestricted to planar 3-regular graphs. We show how the position of the sourceand sink together with the graph geometry and its modifications affect theexcitation transport. This gives us a deep insight into processes whereelongation or addition of dead-end subgraphs may surprisingly result inenhanced transport and we design graphs exhibiting this pronounced behavior. Insome cases this even provides closed-form formulas for the asymptotic transportprobability in dependence on some structure parameters of the graphs.

Key graph properties affecting transport efficiency of flip-flop Grover percolated quantum walks