Physical Correspondences in Quantum Field Theory

E. V. Krishnamurthy, Vikram Krishnamurthy

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.

Gerd Niestegge

Giacomo Mauro D’Ariano

Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can physics be simulated by a quantum computer? Do we believe that a quantum field is ultimately made of a numerable set of quantum systems that are unitarily interacting? A positive answer to these questions corresponds to substituting QFT with a theory of quantum cellular automata (QCA), and the present work is examining this hypothesis. These investigations are part of a large research program on a quantum-digitalization of physics, with Quantum Theory as a special theory of information, and Physics as emergent from the same quantum-information processing. A QCA-based QFT has tremendous potential advantages compared to QFT, being quantum ab-initio and free from the problems plaguing QFT due to the continuum hypothesis. Here I will show how dynamics emerges from the quantum processing, how the QCA can reproduce the Dirac-field phenomenology at large scales, and the kind of departures from QFT that that should be expected at a Planckscale discreteness. I will introduce the notions of linear field quantum automaton and local-matrix quantum automaton, in terms of which I will provide the solution to the Feynman's problem about the possibility of simulating a Fermi field with a quantum computer.

Giacomo Mauro D’Ariano

Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can physics be simulated by a quantum computer? Do we believe that a quantum field is ultimately made of a numerable set of quantum systems that are unitarily interacting? A positive answer to these questions corresponds to substituting QFT with a theory of quantum cellular automata (QCA), and the present work is examining this hypothesis. These investigations are part of a large research program on a "quantum-digitalization" of physics, with Quantum Theory as a special theory of information, and Physics as emergent from the same quantum-information processing. A QCA-based QFT has tremendous potential advantages compared to QFT, being quantum "ab-initio" and free from the problems plaguing QFT due to the continuum hypothesis. Here I will show how dynamics emerges from the quantum processing, how the QCA can reproduce the Dirac-field phenomenology at large scales, and the kind of departures from QFT that that should be expected at a Planck-scale discreteness. I will introduce the notions of linear field quantum automaton and local-matrix quantum automaton, in terms of which I will provide the solution to the Feynman's problem about the possibility of simulating a Fermi field with a quantum computer.

Jayant Vishnu Narlikar, Τ. Padmanabhan