Discover how the Luhn Algorithm verifies credit card accuracy, supports secure transactions, and helps prevent errors in inputting Social Security numbers.

Abstract: By deploying a large number of antennas with sub-half-wavelength spacing in a compact space, dense array systems (DASs) can fully unleash the multiplexing and diversity gains of limited ...

The courses are self-paced and open to learners with or without prior coding experience. Harvard University is offering its most popular computer science courses free of cost to anyone looking to ...

The original version of this story appeared in Quanta Magazine. Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price.

All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don’t need to think about it ...

Quantum computers are coming. And when they arrive, they are going to upend the way we protect sensitive data. Unlike classical computers, quantum computers harness quantum mechanical effects — like ...

Google’s Willow quantum computer (pictured here) is delivering. Image credits: Google. “Today, we’re announcing research that shows — for the first time in history — that a quantum computer can ...

Designed to accelerate advances in medicine and other fields, the tech giant’s quantum algorithm runs 13,000 times as fast as software written for a traditional supercomputer. A quantum computer at ...

Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price. Unhappy with their meager profits, they meet one night in a ...

Google researchers have made a fresh claim of quantum advantage — the ability of quantum computers to radically speed up calculations compared with their classical counterparts. This is not the ...

The new quantum computing algorithm, called "Quantum Echoes," is the first that can be independently verified by running it on another quantum computer. When you purchase through links on our site, we ...