  It is easily seen that the mere existence of an optimal quantum computational
speedup logically implies the mutually exclusive or of well-defined causal
loops. In each of them, it is as if the problem-solver knew in advance one of
the possible halves of the information about the solution she will produce and
measure in the future and used this knowledge to produce the solution with
correspondingly fewer computation steps. Involving only the measurements of
commuting observables, quantum algorithms are submitted to the same (classical)
logic and should therefore host the quantum superposition of the causal loops
in question. However, being causal in character, their ordinary quantum
description cannot describe causal loops. We argue that it must therefore be
incomplete and show that it is completed by time-symmetrizing it. This leaves
the ordinary quantum description mathematically unaltered but replaces its
single causal process by the quantum superposition of causal loops in question.
In their completed quantum description, quantum algorithms respond to the
pre-scientific notion of teleological evolution, that is, an evolution toward a
goal (the solution) with an attractor in the goal it will produce in the future
(the solution again). Once applied to the evolutions of the living, this notion
was dismissed with the advent of modern science for the alleged absence of a
physical basis. We show that, under a quantum cosmological interpretation of
the Anthropic Principle, the same quantum superposition of causal loops
underlying the teleological character of quantum algorithms becomes the missing
physical basis of the teleological character of natural evolutions.
