[gus_massa]

It's not a "quantum computer". It's an analog computer instead of a binary computer. It can be simulated with a normal (binary) computer using floating point numbers (remember that the amoeba has a finite precision).

(Form time to time there are articles that try to explain why analog computers are better than binary computers. Usually they assume infinite precision, that is impossible in a real system.)

The article claims that the time is linear, but it use quadratic space. So if you campare thy to simulate the algorithm with a big system in a sequential computer you will get probably cubic run time.

A better way to understand this is that the amoeba uses a good heuristic to solve the TSP in a small case. There are many heuristics out there, so it would be nice to implement this heuristic and compare with all the other one is some kind of standardized example set. It's more easy to find a good solution in a small system.

(Under the hood, the amoeba is a quantum system. But if you consider this a quantum computer then your phone is also a quantum computer.)

[frevd]

Yeah I guess in order to make this into a simulation, one would effectively add all the exponential time back, since it requires all that to "run" an amoeba on a classical computer. In that article they mention the organism communicating across its body, i.e. reacting to stimuli in all parts in a correlated fashion, that is the bit referring to a quantum system. Of course all physical systems are quantum systems (if I actually had a phone that one too yes, although the operating system does not make use of its nature). So there is no question whether we can simulate that algorithm, it cannot be possible without calculating all the parts, and that is no longer linear time.

[gus_massa]

> In that article they mention the organism communicating across its body, i.e. reacting to stimuli in all parts in a correlated fashion, that is the bit referring to a quantum system.

The internal communication inside the cell is classical, not quantic (classic, like your phone). I guess it use some kind of internal hormone, but it may be some signal that propagates in the cell membrane. IANAB.

You can't have a good quantum correlation in something that is as big as a cell (unless you freeze it at ridiculous low temperature that are not posible for now and would kill the cell anyway, or you have a more ordered system like a extremely pure crystal, or you only want some correlation for ridiculous small amount of time).

You can have big entangled systems, but they look more like pair of very clear optic fiber, not like a cell with a lot of water and crap moving randomly inside.

There are also some interesting "big" quantum effects in molecules like chlorophyll. (I'm not sure if they are 100% confirmad yet.) But a molecule of chlorophyll is much much much smaller than the cell and the effect is very short lived.