Quantum mechanics unlike the rest theories in all experimental sciences involves an extraordinary form of cognition including the measuring apparatus within the studied system. Its knowledge refers to the system of a certain quantum and thus microscopic entity and a macroscopic device by means of the readings of the latter.
The macroscopic device obeys the standard physical conception of causality and time. From the present viewpoint, one can define them mathematically correspondingly as the well-orderability of any set of phenomena linked to each other and constituting a certain whole such as the studied within a certain theory or hypothesis, and the universal well-orderability of all phenomena therefore referring to the wholeness of the world and universe. Time postulating in that way is rather a metaphysical generalization of causality needing furthermore the axiom of choice for its foundation.
However, the system of both quantum entity and apparatus does not obey that standard conception of time and causality. The generally accepted mathematical formalism of quantum mechanics, the separable complex mechanism implies the theorems about the absence of hidden variables (Neumann 1932; Kochen, Specker 1968), which excludes that standard conception as an immediately corollary.
As far as quantum mechanics underlies quantum computation, the latter does not obey it, too.
Any reading of the apparatus is random in principle. Thus, the measured quantum entity cannot cause it within the standard causality, and thus time should be rejected as the system of both quantum entity and apparatus though conserved as to the apparatus standalone. As Wolfgang Pauli demonstrated (1931), time does not possess a corresponding self-adjoint operator as all rest physical quantities (“It is only a number”), and energy conservation does not obey the Heisenberg uncertainty, therefore rejecting Bohr, Kramers, and Slater’s hypothesis (1924).
Interpreted in terms of quantum computation, this means that time refers only the output device of quantum computer, but nevertheless any quantum algorithm is representable as a Turing machine equivalently generating the same states of the output device. Consequently, the quantum computer abbreviates, and thus not more than accelerates the calculation of a Turing machine, but at first glance only. In fact, it can abbreviate an infinite segment of calculation, and thus resolve a problem undecidable in principle by any Turing machine.
Anyway, the statistical ensemble of all possible readings of the apparatus in a moment of time can be postulated as obeying the standard conception of time and causality. That postulate transforms causality in a metaphysical conception experimentally unobservable in principle as to quantum mechanics. Time is a metaphysical hypothesis from the present viewpoint in classical and quantum mechanics.
Interpreted in terms of quantum computation, this postulate means that the quantum computer can be exhaustedly represented by functions mapping a past state into a present or future state. Both past and future state can refer to infinite sets of bits in general, equivalent to qubits. Then, quantum computer is representable a set (infinite in general) of Turing machines in parallel.
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