Where, exactly, could quantum hardware reduce end-to-end training cost rather than merely improve asymptotic complexity on a ...

Noncommutative geometry, at its core, challenges the classical notion of a point by allowing coordinates to fail to commute. This alteration leads to a rich interplay between geometry and algebra, ...

The original version of this story appeared in Quanta Magazine. Hard problems are usually not a welcome sight. But cryptographers love them. That’s because certain hard math problems underpin the ...