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From that question about differences between Quantum annealing and simulated annealing, we found (in comments to answer) that physical implementation of quantum annealing exists (D-Wave quantum computers).
Can anyone explain that algorithm in terms of quantum gates and quantum algorithms, or in physical terms (a part of algorithm that depends on quantum hardware)?
This question should probably go to physics.SE but just as a warning: The D-Wave quantum computer might not really give any speed advancement, because.. something is wrong. So there might not be any physical implementation available so far.
See: Quantum or not, controversial computer yields no speedup, Adrian Cho, Science, 20, 2014, Link
From Wikipedia:
Quantum annealing can be compared to simulated annealing (SA), whose "temperature" parameter plays a similar role to QA's tunneling field strength. However, in SA the neighborhood stays the same throughout the search, and the temperature determines the probability of moving to a state of higher "energy". In QA, the tunneling field strength determines instead the neighborhood radius, i.e. the mean distance between the next candidate state and the current candidate state.
In other words, the "tunneling field" and, indeed, the term "quantum" are just metaphors for the finer points of a completely classical (although randomized) algorithm. QA is not inherently connected with actual quantum computers, it just borrows terms from physics to make a point about computational properties.
