Having lowered the bar for the sense in which we hope to solve a system of linear equations, one might wonder whether this quantum algorithm 3 offers a real advantage over classical computing at all.

To solve an equation, the value of the unknown variable needs to be found. It can be found by performing the same operation on each side of the equation until the value for \(x\) is known.

The company’s AlphaGeometry2 reaches the level of gold-medal students in the International Mathematical Olympiad.

That way it is possible to find the only pair of values that solve both equations at the same time. These are known as simultaneous equations. The unknowns of \(x\) and \(y\) have the same value ...