The unity between quantum field computation, real computation, and quantum computation

摘要

It is indicated that principal models of computation are indeed significantlyrelated. The quantum field computation model contains the quantum computationmodel of Feynman. (The term "quantum field computer" was used by Freedman.)Quantum field computation (as enhanced by Wightman's model of quantum fieldtheory) involves computation over the continuum which is remarkably related tothe real computation model of Smale. The latter model was established as ageneralization of Turing computation. All this is not surprising since it iswell known that the physics of quantum field theory (which includes Einstein'sspecial relativity) contains quantum mechanics which in turn contains classicalmechanics. The unity of these computing models, which seem to have grownlargely independently, could shed new light into questions of computationalcomplexity, into the central P (Polynomial time) versus NP (Non-deterministicPolynomial time) problem of computer science, and also into the description ofNature by fundamental physics theories.