cool!
Quantum computers with maybe 12 or 16 qubits have been built in the lab, but quantum computation is such a young field, and the physics of it are so counterintuitive, that researchers are still developing the theoretical tools for thinking about it.
Systems of linear equations, on the contrary, are familiar to almost everyone. We all had to solve them in algebra class: given three distinct equations featuring the same three variables, find values for the variables that make all three equations true.
Computer models of weather systems or of complex chemical reactions, however, might have to solve millions of equations with millions of variables. Under the right circumstances, a classical computer can solve such equations relatively efficiently: the solution time is proportional to the number of variables. But under the same circumstances, the time required by the new quantum algorithm would be proportional to the logarithm of the number of variables
via Quantum computing may actually be useful, after all.