In these notes about quantum computation by Scott Aronson, he explains that the computation classes $\mathsf{BPP}$ is contained in $\mathsf{BQP}$, but that they are not equal, andSo, the bottom line is that we get a problem -- Simon's problem -- that quantum computers can provably solve exponentially faster than classical computers. Admittedly, this problem is rather contrived, relying as it does on a mythical black box for computing a function f with a certain global symmetry. Because of its black-box formulation, Simon's problem certainly doesn't prove that $\mathsf{BPP} \neq \mathsf{BQP}$. What it does prove that there exists an oracle relative to which $\mathsf{BPP} \neq \mathsf{BQP}$. This is what I meant by formal evidence that quantum computers are more powerful than classical ones.What does he mean by an oracle separation?My understanding of an oracle for a Turing machine is one that solves the halting problem. Surely that can't be the case here?
What is meant by an oracle separation between classes $\mathsf{BPP}$ and $\mathsf{BQP}$?
complexity theory;quantum computing;oracle machines