Relation between quantum computer and quantum field theory?

[erkant]

I'm a computer science and engineering student, who has recently developed interest about quantum computers. I can understand that quantum computers are totally linked with quantum mechanics. But I would like to learn whether there is any relation between quantum computing and quantum field theory? If someone can highlight me the differences between quantum mechanics and quantum field theory, and the possible relations of it with quantum computing, I would be glad.

 

[haael]

Quantum field theory is a relativistic generalization of quantum mechanics. I.e. it incorporates both quantum and relativistic effects.

Quantum computing in principle could be done in plain QM. However, all practical implementations of quantum computing I have seen used the mathematics of QFT. I.e. the braid groups.

Quantum mechanics is a subset of quantum field theory, in a sense. It explains only a limited number od phenomena. If you find a way to do quantum computing on a system that can be described by QM, it would suffice. However, most systems are not that simple.

In the real world, maintaining quantum coherence is tricky, so we can expect that the system that keeps the coherence for the long time enough will need a rather complicated theory to be described. QM may not be enough in this case.

 

[erkant]

Thank you very much haael for a great explanation.