Comment by tsimionescu

So far, the only known algorithm relevant to AI that would run faster on a theoretical quantum computer is linear search, where quantum computers offer a modest speedup (linear search is O(n) on a classical computer, while Grover's algorithm is O(sqrt(n)) for quantum computers - this means that for a list of a million elements, you can scan it in 1 000 steps on a quantum computer instead of 1 000 000 steps on a classical one).

However, even this is extremely theoretical at this time - no quantum computer built so far can execute Grover's algorithm, they are not reliable enough to get any result with probability higher than noise, and anyway can't apply the amount of steps required for even a single pass without losing entanglement. So we are still very very very far away from a quantum computer that could reach anything like the computing performance of a single consumer-grade GPU. We're actually very far away from a quantum computer that even reaches the performance of a hand calculator at this time.