Computational complexity and quantum interpretations

TL;DR

This paper explores how the computational complexity class relationship between BQP and BPP may influence the philosophical interpretation of quantum mechanics, linking physical theory constraints to foundational debates.

Contribution

It proposes that the complexity relationship between BQP and BPP constrains quantum interpretations, suggesting a subjective view favors BQP = BPP, while a realist view implies BPP is a subset of BQP.

Findings

Subjective interpretations favor BQP = BPP.

Realist interpretations imply BPP is a subset of BQP.

Computational complexity may influence quantum foundational perspectives.

Abstract

In computational complexity theory, it remains to be understood whether $\textbf{BQP}$ is the same as $\textbf{BPP}$. Prima facie, one would expect that this mathematical question is quite unrelated to the foundational question of whether the quantum state is an element of reality or of the observer's knowledge. By contrast, here we argue that the complexity of computation in a physical theory may constrain its physical interpretation. Specifically in the quantum case, we argue that a subjective interpretation of the quantum mechanics favors the proposition $\textbf{BQP} = \textbf{BPP}$. Therefore, if $\textbf{BPP} \subset \textbf{BQP}$, then a realist interpretation of quantum mechanics would be favored.