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Quantum field theory and coalgebraic logic in theoretical computer science.

Gianfranco Basti1, Antonio Capolupo2, Giuseppe Vitiello2

  • 1Dipartimento di Filosofia, Università Lateranense, Roma 00184, Italy.

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Summary

Category theory reveals dual equivalence between q-deformed Hopf Coalgebras and Algebras in quantum field theory (QFT). This framework models dissipative quantum systems and inspires novel quantum computing architectures.

Keywords:
Category TheoryFibonacci progressionTheoretical computer scienceThermal quantum field theoryTopological quantum computingq-deformed Hopf Coalgebras

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Category Theory

Background:

  • Quantum field theory (QFT) is extended to thermal field theory.
  • Dissipative quantum systems and far-from-equilibrium conditions require advanced modeling.
  • Applications in neuroscience, such as modeling brain memory capacity, inspire new theoretical frameworks.

Purpose of the Study:

  • To demonstrate the dual equivalence between q-deformed Hopf Coalgebras and q-deformed Hopf Algebras within Category Theory.
  • To model dissipative quantum systems and thermal baths using this dual equivalence.
  • To explore the potential for new quantum computing architectures based on this formulation.

Main Methods:

  • Utilizing Category Theory to establish mathematical and logical dual equivalence.
  • Interpreting algebra-coalgebra pairs as QFT systems and their thermal baths.
  • Applying the concept of Universal Coalgebra to label quantum vacua.

Main Results:

  • Established dual equivalence between q-deformed Hopf Coalgebras and Algebras via a shared functor (related to Bogoliubov transform).
  • Identified the q-deformation parameter as a thermal parameter linked to the Bogoliubov angle.
  • Demonstrated that different q values label unique quantum vacua, interpretable as Final Coalgebras.

Conclusions:

  • The q-deformed Hopf Coalgebra/Algebra framework provides a novel way to model thermal field theories and dissipative quantum systems.
  • This formulation offers a new perspective on quantum vacuum structure and labeling.
  • The approach opens possibilities for designing novel universal quantum computing architectures, evidenced by Fibonacci progression generation.