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At the beginning of a quantum computational process we generally want to start in a perfectly known initial state, and evolve from there. This cannot be done perfectly, for fundamental reasons, but I strongly suspect there has to be a practical limit below which you are in a garbage-in-garbage-out situation.

My full question is not on this input fidelity threshold per se (although feel free to provide that too), but rather on the factors to consider and minimum set(s) of requirements one needs to prepare a good-enough initial state (maybe Di-Vincenzo-list style, but preferrably with some example numbers). Presumably the perfect answer has different sections, for example depending on whether one employs thermal initialization or algorithmic cooling.

For a little more context, this question is related with certain aspects of previous ones:

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