Quantum field theory and computational paradigms

Abstract

We introduce the basic theory of quantization of radiation field in quantum physics and explain how it relates to the theory of recursive functions in computer science. We outline the basic differences between quantum mechanics (QM) and quantum field theory (QFT) and explain why QFT is better suited for a computational paradigm - based on algorithmic requirement, countably infinite degrees of freedom and the creation of macroscopic output objects. The quanta of the radiation field correspond to the non-negative integers and the harmonic oscillator spectra correspond to the recursive computation - with the creation and annihilation operators, respectively, playing the same role as the successor and predecessor in computability theory. Accordingly, this approach relates the classical computational model and the quantum physical model more directly than the Turing machine approach used earlier. Also, the application of Lambda calculus formalism and the associated denotational semantics (that is widely used in the classical computational paradigm involving recursive functions) for applications to computational paradigm based on quantum field theory is described. Finally, we explain where QFT and conventional paradigm depart from each other, and examine the concept of fixed points, phase transitions, programmability, emergent computation and related open problems.