The Quantum-Extended Church-Turing Thesis in Quantum Field Theory

TL;DR

This paper investigates whether quantum field theories like QED challenge the quantum-Extended Church-Turing thesis, concluding that particle creation aligns with quantum parallelism and does not violate the thesis, though some interactions could offer computational advantages.

Contribution

It constructs a QED-inspired computational model showing particle creation does not violate the quantum-Extended Church-Turing thesis and explores potential computational advantages of complex interactions.

Findings

Particle creation aligns with quantum parallelism.

Particle creation does not violate the quantum-Extended Church-Turing thesis.

Certain QED interactions may enable exponential complexity gates.

Abstract

The quantum-Extended Church-Turing thesis has been explored in many physical theories including general relativity but lacks exploration in quantum field theories such as quantum electrodynamics. Through construction of a computational model whose gate set mimics the interactions of QED, we demonstrate that one of the defining features of quantum field theory, particle creation and annihilation, is not likely to violate the quantum-Extended Church-Turing thesis. Through this computational model, it is shown that particle creation is likely only another form of quantum parallelism. However, whether or not the quantum-Extended Church-Turing thesis will hold for all computational devices in quantum field theories is still not known. For example, we briefly examine certain interactions in quantum electrodynamics which may create multi-qubit gates. These gates may have exponential complexity at the cost of being exponentially weak. This may in turn allow for computational advantage over traditional gate sets such as Clifford+T.