  In computational complexity theory, it remains to be understood whether
$\textbf{BQP}$ is the same as $\textbf{BPP}$. Prima facie, one would expect
that this mathematical question is quite unrelated to the foundational question
of whether the quantum state is an element of reality or of the observer's
knowledge. By contrast, here we argue that the complexity of computation in a
physical theory may constrain its physical interpretation. Specifically in the
quantum case, we argue that a subjective interpretation of the quantum
mechanics favors the proposition $\textbf{BQP} = \textbf{BPP}$. Therefore, if
$\textbf{BPP} \subset \textbf{BQP}$, then a realist interpretation of quantum
mechanics would be favored.
