> It almost makes it sound like there will be some algorithms that quantum is better at and that they won't necessarily be the same algorithms that "classical"

> It almost makes it sound like there will be some algorithms that quantum is better at and that they won't necessarily be the same algorithms that "classical" computing uses. This is exactly correct. While you can simulate classical computations on a quantum computer, it doesn't make a lot of sense to. However, there exists a class of problems for which there exist solutions that have lower time complexities than anything we can run on a classical computer, if only we had a quantum computer of sufficient size. Examples of such algorithms are the famous two, Shor's and Grover's algorithms, of which Shor's is more interesting because it factors integers in polynomial time whereas the best known classical algorithm runs in exponential time (this is the one that's scary for cryptography). Grover's algorithm is basically function inversion (find the x given a function f and some desired value y such that f(x)=y) in O(sqrt(N)) over the domain of the function, which on a classical computer requires O(N) operations. Those were discovered in the 90's, so they're pretty widely understood by now. There's a few newer ones, such as the quantum algorithm for linear systems of equations, which solves for a scalar result of an operation applied to the unknown vector x such that Ax=b in O(log(N)k^2) time versus the classical O(nk), where n is the number of matrix elements and k is a measure of how sensitive to error the problem is. Basically, there's a handful of useful algorithms, and another dozen or so theoretically interesting ones, that can run faster on a quantum computer. For everything else, there's zero advantage to using one.