Computational complexity

Three computer scientists have posted a proof of the NLTS conjecture, showing that systems of entangled particles can remain difficult to analyze even away from extremes.

Why verify every line of a proof, when just a few checks will do?

Finding out whether a question is too difficult to ever solve efficiently depends on figuring out just how hard it is. Researchers have now shown how to do that for a major class of problems.

Cryptographers want to know which of five possible worlds we inhabit, which will reveal whether truly secure cryptography is even possible.

The existence of secure cryptography depends on one of the oldest questions in computational complexity.

For years, intermediate measurements made it hard to quantify the complexity of quantum algorithms. New work establishes that those measurements aren’t necessary after all.

Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits.

The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem.

To understand what quantum computers can do — and what they can’t — avoid falling for overly simple explanations.