  We consider the problem of strong (amplitude-wise) simulation of $n$-qubit
quantum circuits, and identify a subclass of simulators we call monotone. This
subclass encompasses almost all prominent simulation techniques. We prove an
unconditional (i.e. without relying on any complexity theoretic assumptions)
and explicit $(n-2)(2^{n-3}-1)$ lower bound on the running time of simulators
within this subclass. Assuming the Strong Exponential Time Hypothesis (SETH),
we further remark that a universal simulator computing any amplitude to
precision $2^{-n}/2$ must take at least $2^{n - o(n)}$ time. Finally, we
compare strong simulators to existing SAT solvers, and identify the
time-complexity below which a strong simulator would improve on
state-of-the-art SAT solving.
