Therefore, one may feel compelled to use digital methods for implementing unnatural interactions in the controllable system, based on the decomposition of the exact unitary evolution into a sequence of discrete gates [2].
Then, we make use of the Trotter expansion [2 4] to decompose the unitary evolution of the simulated system in a sequence of quantum gates.
Thus once the black hole has completely evaporated away, the entropy of the universe will have increased — in violation of unitary evolution).
If one begins with a system in a precisely known quantum state, then unitary evolution guarantees that the details about that system will evolve in such a way that one can infer the precise quantum state of the system at some later time (as long as one knows the law of evolution and can perform the relevant calculations), and vice versa.
Measurement-based algorithms differ from the circuit model in that instead of applying unitary evolution as the basic mechanism for the manipulation of information, these algorithms use only non-unitary measurements as their computational steps.
I figured if the very movement of the pieces was implemented using unitary evolution (fancy words for how quantum things change) in a way that created superposition, then other quantum phenomena would manifest.
In this paper, we give an algorithm for the control of the unitary evolution operator for the system of two spin 12's interacting through Heisenberg interaction.
Collapses interrupt or outright replace the unitary evolution of the quantum state.
(It should be noted that 'quantum computing,' in the standard modern sense, is based on the predictability of the unitary evolution, and does not, as yet, go into the question of how reduction occurs).
The challenge of saving information from a black hole lies in the fact that it is impossible to copy the quantum details (especially the quantum correlations) that are preserved by unitary evolution.
