  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.
