Solving a billion equations with a billion variables in nine seconds!

Ran across something interesting yesterday.

Currently the fastest way to solve multiple equations with multiple unknowns is to place them into a matrix, then reduce the matrix to it's simplest form. We call this matrix an "N by N" square matrix, where the number of equations match the number of unknowns in a one to one ratio. This goes very fast for matrices which are less then 9 by 9. Nine equations, nine unknowns. However, as you start increasing N it takes longer and longer to solve these types of matrices. That's even with using a computer. Forget trying to do these by hand!

If you had a N = 1,000,000,000. Current algorithms would take at least one second per equation, meaning it would take one billion seconds to solve this, or 32 years. However Mathmaticitians have developed an algorithm that uses the theory of quantum computing to break the solve time to instead of a second per equation, to a second per digit of N (number of equations).

If you have a billion equations (1,000,000,000) you have nine digits more than one. A N of say a trillion would take 12 seconds. A N of a thousand would take 3 seconds.

This is pretty cool stuff. If we already let the computer solve matrices that take say one hour. Then with this we could solve a matrix with 3600 digits for N. That's a 1 with 3,600 zeros behind it, or 1,200 sets of zeros or 1x10^3,600th power. A google is just 1x10^100!  That's pretty staggering.

If anyone wants to come up with a name for that number, by all means. Maybe a contest? "The best name for the number 1x10^3,600".

source: http://io9.com/5443389/mathematicians-create-algorithm-so-complex-no-computer-can-use-ityet