# quantum computer and nonlinear mathematics?

Does a quantum computer also instantaneously find solutions to any given (nonlinear) equation or system of equations?

### 3 Answers

- BiofreakLv 61 decade agoFavorite Answer
I agree... no. But I'm not sure what you mean by 'also', since a quantum computer doesn't instantaneously find solutions to anything. There is nothing instantaneous about it. For example, Grover's algorithm, which is used for doing unstructured search, uses an iterative process where it amplifies the population in a 'correct' state. The more times the algorithm is run, the more population moves to the correct state. The benefit is that the algorithm needs to be run fewer times to get a reasonable probability of getting the correct answer than a comparable classical algorithm. Fewer times... not a single time. Same with the quantum Fourier transform which is part of the Shor factoring algorithm. The point is these quantum algorithms require fewer steps, but nothing about them is instantaneous. As far as solving nonlinear problems, there are a limited number of problems for which there is a known quantum algorithm. So there are a limited number of problems for which a quantum computer will be of benefit. And the main ones are factoring and unstructured search. For an arbitrary nonlinear problem, there is no algorithm, so there is no known way that a quantum computer will help.

- 6 years ago
So what about quantum annealing?

- Anonymous1 decade ago
No