This is just not the case, even with infinite energy and time. There are properties of quantum Turing machines that are not reproducible with classical Turing machines.
https://web.archive.org/web/20081123183419/http://www.ceid.u...
https://web.archive.org/web/20081123183419/http://www.ceid.u...
(If there is more than the abstract there, the scrolling isn’t working on my phone.)
There is no function that a QTM can compute that a TM cannot. But a QTM can compute some functions much faster.
Or, as phrased in the abstract “these do not include the computation of any non-recursive function”.
Edit: of course, there are things that can can be done with QM that can’t be with a TM (such as the entangled multi-party prover/verifier setup), but none of them are “compute this function (with no limit on how long it takes)” or “simulate this situation (with no limit on how long it takes)”