Quantum cellular automata and free quantum field theory

In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit

Giacomo Mauro D’Ariano; Paolo Perinotti

2016

Scholarcy highlights

  • Quantum information theory has represented a new way of looking at foundations of Quantum Theory, and the study of quantum protocols has provided a significant reconsideration of the of the structure of the theory, which eventually resulted in a new axiomatization program, initiated in the early 2000
  • The starting idea is to look at physical laws as an effective description of an information processing algorithm, which updates the states of an array of quantum memory cells, with particles emerging as the interpretation of special patterns of the memory
  • In this paper we review the derivation from principles of previous research, proving in detail that the graph of the quantum cellular automaton is a Cayley graph of a finitely presented group, and showing how for the case corresponding to an Euclidean emergent space the automata lead to Weyl, Dirac and Maxwell field dynamics in the relativistic limit
  • We conclude with some perspectives towards the more general scenario of nonlinear automata for interacting quantum field theory
  • In the previous sections we showed how the dynamics of free relativistic quantum fields emerges from the evolution of states of Fermionic QCAs, provided that they satisfy the requirements of unitarity, linearity, homogeneity and isotropy
  • In the previous sections we showed how the dynamics of free relativistic quantum fields emerges from the evolution of states of Fermionic quantum cellular automaton, provided that they satisfy the requirements of unitarity, linearity, homogeneity and isotropy

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