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I just stumbled upon this research paper https://arxiv.org/abs/2309.16596.

They claim to have found a problem which is easy to solve quantumly but hard classically: to find local minima of 2D Hamiltonians (which turns out to be all the same). From a quick reading, it seems to me that this requires what they call "thermal perturbation", i.e. a thermodynamics process due to the Lindbladian operator (which is irreversible).

Doesn't this contradict the assumption that all quantum evolution should be unitary (and hence always reversible)?

I can imagine that this is realizable only in a future where, together with the current quantum computers we have, we could couple a way of simulating this "thermal perturbation". Has someone already gone through it and can explain to me better if I understood correctly?

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The postulate that all quantum evolutions are unitary applies to the case of closed systems. The Lindbladian form comes into picture when we are discussing about open systems. In this case, where there is a thermal perturbation, as they have mentioned in the paper(page 2), there is an interaction between the system and a thermal bath. So the system we want to study here is not a closed system.

If we would have considered the evolution of the entire System-Environment state, that would be a closed system and thus the evolution would be represented by an unitary operator.

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