zlacker

Many problems require lots of huge matrix multiplications—think simulations of physical systems, i.e. weather systems or molecular interactions, or numerical optimization.

>>skosch+(OP)
Additionally, many problems are can be converted to matrix operations, like graph algorithms.

Note that matrix multiplication takes O(n^2) time with a quantum computer, but O(n^2.807) time on a classical computer.

>>TJSome+ga
> but O(n^2.807) time on a classical computer

Optimizing matrix multiplication for classical computers is an open research problem, and according to wikipedia there are algorithms with O(n^2.37) running time. Also according to wikipedia, it is not proven that matrix multiplication can't be done in O(n^2).

>>gnu-no+re
Ah yes, we may as well add NP-completeness to this thread.