Is it possible to create a human thinking and acting program on a computer?
Quantum computers have the same power as classical computers, only they can apparently solve some problems much faster. In order to simulate a human, you need to consider two aspects:


Cognitive aspect: The program should behave like a human being.
Physical aspect: The object should look like a human being.


Turing suggested a way of sidestepping the second issue. He suggested limiting the interaction to a text-based "chat". Even in this case, the computer has to careful regarding reaction times: the computer can presumably type faster than a human and perform calculations faster. 

There are several variants of the Turing test, but one of them involves many testers and two interviewees: a bona fide human and a computer. The computer is trying to pass as human. An interviewer gets assigned either the human or the computer, and should guess which is which. The computer passes the Turing test if the interviewer guesses no better than a random coin toss.

Current computers are not able to pass the Turing test. Whether they could potentially pass the test is at this point a philosophical and religious question. One advantage that humans have over computers is their large brain and their long learning period. However, if we could build large enough computers, so far we don't understand the algorithmic behavior of the brain, and so cannot mimic it. Artificial intelligence tries to ape human intelligence using different "hardware". Whether this approach can be successful or not is not clear.

In the past few decades, focus has switched from trying to emulate the brain to trying to solve certain tasks, such as translation. Modern techniques use statistical tools that are not aimed at mimicking behavior but only at mimicking competence. This approach works much better than earlier approached which did try to understand what human cognitive processes are based on. Perhaps this approach is hopeless if the goal is passing the Turing test.

So what is missing for artificial intelligence to succeed? Higher processing power? Computation techniques mimicking brain functions? Mechanisms like the Universal Grammar which might be hiding in our genes? Nobody knows. But for many people, there is no theoretical barrier, only practical ones.