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

We present two results on the subject of quantum contextuality andcohomology, and non-locality and quantum advantage with shallow circuits.Abramsky et al. showed that a range of examples of quantum contextuality isdetected by a cohomological invariant based on \v{C}ech cohomology. However,the approach does not give a complete cohomological characterisation ofcontextuality. A different cohomological approach to contextuality wasintroduced by Okay et al. Their approach exploits the algebraic structure ofthe Pauli operators and their qudit generalisations known as Weyl operators. Wegive an abstract account of this structure, then generalise their approach toany example of contextuality with this structure. We prove at this generallevel that the approach does not give a more complete characterisation ofcontextuality than the \v{C}ech cohomology approach.  Bravyi, Gosset, and K\"{o}nig (BGK) gave the first unconditional proof that arestricted class of quantum circuits is more powerful than its classicalanalogue. The result, for the class of circuits of bounded depth and fan-in(shallow circuits), exploits a particular family of examples of contextuality.BGK's quantum circuit and computational problem are derived from a family ofnon-local games related to the well-known GHZ non-local game. We present ageneralised version of their construction. A systematic way of taking examplesof contextuality and producing unconditional quantum advantage results withshallow circuits.

Comparing two cohomological obstructions for contextuality, and a generalised construction of quantum advantage with shallow circuits