Are ordinary desktop computers complex systems? I’m taking complex systems course and we should have chosen a complex system and write a report about it. I chose computer as my complex system and explained about it, but my teacher argued that because ordinary computers work serially or because for example when CPU doesn’t work there isn’t any output for the system, and etc. ordinary computers are simple systems and instead quantum computers are complex systems.

A complex system is a system formed out of many components whose
  behavior is emergent, that is, the behavior of the system cannot be
  simply inferred from the behavior of its components. The amount of
  information necessary to describe the behavior of such a system is a
  measure of its complexity.
  Yaneer Bar-Yam, Dynamics of Complex Systems

My question is that is it really true that desktop computers aren’t complex systems (I think it’s not true) and if it is true, then what are the main and the most important factors that make quantum computers complex systems? Can anyone please explain about computers as complex systems and factors or elements that prove their complexity.
 A: I'm not an expert but from what I found out on the web about complex systems I would like to argue in favor of computer (hardware and software) being a complex system. The properties needed for a complex system are : 


*

*Feedback loops- Ordinary desktop computers have feedback loops the best example is adaptive softwares. 

*Spontaneous order- The colorful monitor is a result of individual pixels working together to mix different RGB combinations to give a different color which is controlled by a transistors.

*Robustness- ability to withstand failure. A computer can automatically back up all information in case of a failure and retrieve it at a later stage. The warning of low battery in laptop is an example of robustness too.

*Emergence is obvious.

*Hierarchy can be pointed out if emergence and large number of tiny components are present. Computers have a definite hierarchy. Atoms form transistors that form gates that form micro-architecture that form.... it goes on until the computer is applied to solve problems!

*Numerosity- It's obvious. There are thousands of tiny "transistor cities" on that small chip. These are responsible for the emergent behavior of computers.
Definitely quantum computers would be a more complex system that applies different kinds of physics to operate but if we say that an ordinary computer is not a complex system then neither is the human body. 
You can argue with your teacher by drawing all the similarities between human body and an ordinary computer (I think we did it in middle school when we were introduced to computers). 
To tackle the point raised by your teacher that when the CPU isn't working nothing works you should tell her that the CPU is like the brain of the computer. If a human brain isn't working then there is paralysis or even muscle atrophy. The other components of the body don't stop working but they lose the coherence! The same is the case in computers. A monitor will still display images when the CPU is malfunctioning, it's just that it won't show the images that we need. And I disagree that computers work serially. The components have different power sources that can operate on their own if they're disconnected from the CPU. We need the CPU to get a coherent output that we can appreciate.
My suggestion is that you can just draw out the similarities between human body and a computer. And I hope it helps. :) 
A: I think this question is not particularly to do with Physics.  Here are a couple of answers nonetheless.
(Note that this is a heavily revised version of my original answer, which talked about simulating brains: this version is intended to not require any AI-related philosophical arguments.)
A computer and its software can be a complex system


*

*Let's consider a system that everyone agrees is complex: for instance the weather systems on a planet;

*A computer is effectively a Turing-equivalent machine: although a computer is in fact a finite-state machine, you can add more storage (tape for the TM) indefinitely, and any program that halts on specified arguments uses only a finite number of states and thus can be computed by a FSM.

*A program can be written which can simulate weather systems to any required degree of accuracy.  This program can run on a suitably-configured computer (ie it does not need unbounded storage or time).

*This program, together with the machine on which it runs, is therefore a complex system.


The weak point in this argument, for weather systems anyway, is (3), and there are two arguments against it, both of which I will now address and dismiss.
Chaos
We know that weather exhibits dynamical chaos, and thus we could naively claim that, in fact, a computer program can't simulate a weather system to 'any required degree of accuracy': because tiny differences in initial conditions will cause the simulation to diverge rapidly from the real system.
This is to misunderstand what I mean by 'simulate': it is not necessary to copy a particular weather system, it is merely necessary to run a simulation which is as good as you like a siulation of some weather system.  At the point where the simulation is accurately modelling individual raindrops it does not really matter whether they are the same raindrops as in the real world or indeed whether it is raining at all in the real world: the simulation is good enough (or if it is not, pile more computing power into it until it is).
The requirement should be that you can't tell if the system you are observing is simulated or real, not that the simulation accurately follows the evolution of a particular real system.
Simulations don't halt
This is easier to dismiss: obviously it it true, but uninteresting.  While the simulation does not halt, the computation of each timestep in the simulation both does halt, and requires only bounded resource: the program that computes the state vector of the system $S(t+\delta t)$ as a function of $S(t)$ does halt and requires only bounded resource (in particular: can be implemented by a finite state machine, since it halts).
You don't need a quantum computer
Since a quantum computer is not properly more powerful (can not compute anything a conventional TM can not compute) then the argument that only quantum computers are complex would need to rely on the speedup that quantum computers can achieve.
So any argument that a quantum computer is needed would require it somehow not to be possible to run a simulation of a weather system at constant time per step.  But obviously you can do this, so long as you are happy for your simulation to be merely realistic rather than for its evolution to correspond to a particular physical weather system, as I said above.
The reason you can do this is simple: if you can model a single step in constant time, then you just restart the model with the new state as its initial conditions, and you can therefore model the next step in the same constant time.  So there is at most a constant factor slowdown over the real system.
(The reason you might need a quantum computer if you want your model's evolution to follow the real evolution of the system is that you need more and more precision as time goes on.  I suspect in fact that a quantum computer does not help with this, but it's beside the point here.)

I'm now going to vote for this question to be closed as off-topic (yes, I am being inconsistent here).
