Limiting the complexity of quantum states: a toy theory

TL;DR

This paper proposes a toy theory that limits quantum state complexity by restricting the number of interactions per qubit within the circuit model, exploring its consistency and experimental implications.

Contribution

It introduces a novel restriction on quantum states based on interaction limits, providing a consistent toy model within the circuit framework.

Findings

The toy theory is consistent within the circuit model.

It can replicate phenomena observed in quantum experiments.

Extension beyond the circuit model faces conflicts with observed facts.

Abstract

This paper discusses a restriction of quantum theory, in which very complex states would be excluded. The toy theory is phrased in the language of the circuit model for quantum computing, its key ingredient being a limitation on the number of interactions that \textit{each} qubit may undergo. As long as one stays in the circuit model, the toy theory is consistent and may even match what we shall be ever able to do in a controlled laboratory experiment. The direct extension of the restriction beyond the circuit model conflicts with observed facts: the possibility of restricting the complexity of quantum state, while saving phenomena, remains an open question.