Function that grows faster then BB(n) using quantum computation?

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Is it possible to define a function in terms of quantum computers that grows faster then any that is defined in terms of turing machines?

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No, a quantum computer can be simulated by a classical one, and hence anything that can be computed by a quantum computer can also be computed by a Turing machine.

The classical computer might take much longer than the quantum one, but the final result of the computation would be the same.