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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider Shor's quantum factoring algorithm in the setting of noisyquantum gates. Under a generic model of random noise for (controlled) rotationgates, we prove that the algorithm does not factor integers of the form $pq$when the noise exceeds a vanishingly small level in terms of $n$ -- the numberof bits of the integer to be factored, where $p$ and $q$ are from awell-defined set of primes of positive density. We further prove that withprobability $1 - o(1)$ over random prime pairs $(p,q)$, Shor's factoringalgorithm does not factor numbers of the form $pq$, with the same level ofrandom noise present.

Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise