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

The $p$-stage Quantum Approximate Optimization Algorithm (QAOA$_p$) is apromising approach for combinatorial optimization on noisy intermediate-scalequantum (NISQ) devices, but its theoretical behavior is not well understoodbeyond $p=1$. We analyze QAOA$_2$ for the maximum cut problem (MAX-CUT),deriving a graph-size-independent expression for the expected cut fraction onany $D$-regular graph of girth $> 5$ (i.e. without triangles, squares, orpentagons).  We show that for all degrees $D \ge 2$ and every $D$-regular graph $G$ ofgirth $> 5$, QAOA$_2$ has a larger expected cut fraction than QAOA$_1$ on $G$.However, we also show that there exists a $2$-local randomized classicalalgorithm $A$ such that $A$ has a larger expected cut fraction than QAOA$_2$ onall $G$. This supports our conjecture that for every constant $p$, there existsa local classical MAX-CUT algorithm that performs as well as QAOA$_p$ on allgraphs.

Local classical MAX-CUT algorithm outperforms $p=2$ QAOA on high-girth regular graphs