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

The clique problems, including $k$-CLIQUE and Triangle Finding, form animportant class of computational problems; the former is an NP-completeproblem, while the latter directly gives lower bounds for MatrixMultiplication. A number of previous efforts have approached these problemswith Quantum Computing methods, such as Amplitude Amplification. In this paper,we provide new Quantum oracle designs based on the 1-factorization of completegraphs, all of which have depth $O(n)$ instead of the $O(n^2)$ presented inprevious studies. Also, we discuss the usage of one of these oracles inbringing the Triangle Finding time complexity down to $O(n^{2.25} poly(logn))$, compared to the $O(n^{2.38})$ classical record. Finally, we benchmark thenumber of required Amplitude Amplification iterations for another presentedoracle, for solving $k$-CLIQUE.

Using 1-Factorization from Graph Theory for Quantum Speedups on Clique Problems