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 investigate the $\Lambda$-polytopes, a convex-linear structure recentlydefined and applied to the classical simulation of quantum computation withmagic states by sampling. There is one such polytope, $\Lambda_n$, for everynumber $n$ of qubits. We establish two properties of the family $\{\Lambda_n,n\in \mathbb{N}\}$, namely (i) Any extremal point (vertex) $A_\alpha \in\Lambda_m$ can be used to construct vertices in $\Lambda_n$, for all $n>m$.(ii) For vertices obtained through this mapping, the classical simulation ofquantum computation with magic states can be efficiently reduced to theclassical simulation based on the preimage $A_\alpha$. In addition, we describea new class of vertices in $\Lambda_2$ which is outside the knownclassification. While the hardness of classical simulation remains an openproblem for most extremal points of $\Lambda_n$, the above results extendefficient classical simulation of quantum computations beyond the presentlyknown range.

On the extremal points of the $\Lambda$-polytopes and classical simulation of quantum computation with magic states