Simulation Quantization: An Application of Physical Versions of the Church-Turing Thesis

TL;DR

This paper explores the relationship between classical and quantum simulation of anharmonic oscillators, proposing that quantum simulation entails quantization and discussing implications for the Church-Turing thesis.

Contribution

It introduces the concept of simulation quantization, linking classical simulation capabilities to quantum quantization and analyzing conditions under which systems are quantizable.

Findings

Classical simulability suggests quantum simulability and quantization.

Certain anharmonic oscillators are not quantizable due to their Hamiltonian structure.

Obstructions to quantization are argued to be purely quantum phenomena.

Abstract

An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not quantizable. If, as argued here, quantum simulation of a finitely realizable classical physical system entails quantization of that system, then either there exist nonsimulable, integrable anharmonic oscillators or there are no obstructions to quantization by simulation. Simulation quantization implies further that any obstructions to quantization arise entirely within the quantum domain.