Quantum fermions from classical bits

TL;DR

This paper demonstrates that a simple probabilistic cellular automaton can replicate relativistic fermionic quantum field theories, bridging classical statistical systems and quantum mechanics, and suggesting potential for classical quantum computing implementations.

Contribution

It introduces a classical probabilistic automaton that models relativistic fermions and derives quantum concepts from classical statistical systems, offering new insights into quantum-classical correspondence.

Findings

Automaton reproduces fermionic quantum field theory behavior

Quantum concepts emerge naturally from classical probabilistic automaton

Potential for classical probabilistic models to simulate quantum computing

Abstract

A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically on bit configurations. The genuinely probabilistic character of quantum physics is realized by probabilistic initial conditions. In turn, the probabilistic automaton is equivalent to the classical statistical system of a generalized Ising model. For a description of the probabilistic information at any given time quantum concepts as wave functions and non-commuting operators for observables emerge naturally. Quantum mechanics can be understood as a particular case of classical statistics. This offers prospects to realize aspects of quantum computing in the form of probabilistic classical computing.