In other words, there would be efficient quantum algorithms that perform tasks that do not have efficient probabilistic algorithms. This would not however invalidate the original Church–Turing thesis, since a quantum computer can always be simulated by a Turing machine, but it would invalidate the classical complexity-theoretic Church–Turing thesis for efficiency reasons. Consequently, the quantum complexity-theoretic Church–Turing thesis states:[1] "A quantum Turing machine can efficiently simulate any realistic model of computation."