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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Quantum walk algorithms can speed up search of physical regions of space inboth the discrete-time [arXiv:quant-ph/0402107] and continuous-time setting[arXiv:quant-ph/0306054], where the physical region of space being searched ismodeled as a connected graph. In such a model, Aaronson and Ambainis[arXiv:quant-ph/0303041] provide three different criteria for a unitary matrixto act locally with respect to a graph, called $Z$-local, $C$-local, and$H$-local unitaries, and left the open question of relating these threelocality criteria. Using a correspondence between continuous- and discrete-timequantum walks by Childs [arXiv:0810.0312], we provide a way to approximate$N\times N$ $H$-local unitaries with error $\delta$ using$O(1/\sqrt{\delta},\sqrt{N})$ $C$-local unitaries, where the comma denotes themaximum of the two terms.

On the relationships between Z-, C-, and H-local unitaries