Quantum computers dance a reversible waltz: step forward — step back, and the system returns to its starting point. But in some processes, the dancer vanishes into darkness, never to return. Such irreversible steps add entropy to the system — a measure of irreversible disorder. If a quantum computer could easily perform such tricks, it would solve problems that would take ordinary machines an eternity. This would violate all known rules of computational complexity. Yet the same logic suggests: there are no easy paths. Strikingly, a similar irreversible loss of information occurs with black holes, and this puzzle forced Hawking to reconsider his own views. Nature abhors a free lunch — even in the quantum world.