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

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.