# Threshold and practical requirements for initial state preparation?

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:

I'm probably late to party but I found this section today. In terms to answer your question[s] I made a lot of thoughts and read enough paper for a tree.

I found 2 excellent experiments (very timely) that show their practical testing problems and solutions. And most important their preparation for a reproducible quantum state. The documentations of both projects are really well written. I see no need of just copying and paste it here or describe it by myself and leaving out to many details. I enjoyed reading it and will provide it to you for better preparation in the future.

1. Project: Low-depth Quantum State Preparation at 15 March 2021 (China)

This Team investigate this space-time tradeoff in quantum state preparation with classical data. Trying Positive label state preparation and Arbitrary state preparation.

2. Project: Automatic Preparation of Uniform Quantum States Utilizing Boolean Functions in 2019 (Switzerland)

The second Team investigate the automatic state preparation of a specific subset of arbitrary quantum states that are uniform superpositions over a subset of basic states. Some of them can be represented using boolean functions.

Interesting at this project is that they found an upper bound on the number of quantum gates in the {Ry(θ), CNOT} gate set. In their experiment the quantum state preparation affords at most 2ⁿ − 1 Ry rotation gates and 2ⁿ − 2 CNOTs

This answer is intended to provide an insight into practical quantum computing preparation and generate fix points to serve as reference and zero point.