Quantum Energy-based P Systems

Energy–based P systems have been recently defined as P systems in which the amount of energy manipulated and/or consumed during computations is taken into account. In this paper we propose two quantum versions of energy–based P systems. Both versions are defined just like classical energy–based P systems, but for objects and rules. Objects are represented as pure states in the Hilbert space C^d, whereas the definition of rules differs between the two models. In the former, rules are defined as bijective functions — implemented as unitary operators — which transform the objects from the alphabet. In the latter, rules are defined as generic functions which map the alphabet into itself. Such functions are implemented using a generalization of the Conditional Quantum Control technique, and may yield to non–unitary operators. Finally, we address some problems and outline some directions for future work.