# Can quantum computers be modelled as a classical computer with access to an oracle?

Quantum computers can solve certain problems faster than classical computers e.g factoring numbers.

and this is because quantum computers can do a fourier transform on $$n$$ bits in $$O(n^2)$$ time as opposed to $$O(n2^n)$$ time.

We can usually reduce time complexities by pretending that we can do some thing faster - introducing oracle's that can solve a problem instantly.

Is there an oracle that encoded all the quantum speed ups we get?

Vacuous answer: because $$\text{BPP}^\text{BQP} = \text{BQP}$$, giving a computer access to a $$\text{BQP}$$ oracle makes it equivalent to a quantum computer at solving decision problems in polynomial time. This is sort of like saying "if your computer has access to a quantum computer, then you have access to a quantum computer" but it does meet the criteria in your question.
Also, quantum computers can't do a Fourier transform on $$2^n$$ bits in $$O(n^2)$$ time. Quantum computers can apply a Fourier transform to the state vector of $$n$$ qubits in $$O(n^2)$$ time. It's not at all the same thing.