Abstract: Integrated information theory (IIT), in its present form, lacks a defined ontology. That said, in IIT version 3.0, working examples are constructed using autonomous Boolean networks. The development of a quantum IIT (qIIT) for which classical IIT is some kind of limiting case, adds additional requirements to any potential ontology such as Boolean networks. The relatively straightforward manner by which Boolean networks can be adapted to quantum inputs as well as their complex and emergent features, make them attractive in this regard. But exactly how to go about adapting these networks to the quantum case relies, at least in part, on the nature of measurement and, in particular, exactly when (or even if) it occurs. Two solutions to this problem are presented and compared within the context of IIT.