Modeling and Analysis of Margolus Quantum Cellular Automata Using Net-Theoretical Methods

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Petri net methods have been very successful in modeling the operation of classical parallel systems. In this work, these methods are applied to designing semi-classical parallel quantum computers. The demonstration object of our study is a quantum Billiard Ball Model Cellular Automaton (bbmca) suggested by Margolus. Firstly, a high-level Petri net model of a classical reversible version of this automaton is constructed. Subsequently, this Petri net model is used as a so-called kernel net of the quantum bbmca. The time-independent Hamiltonian needed to generate the time-evolution of a quantum computer can be automatically generated from the reachability graph of a kernel net. Also, a new numerical method for solving the resulting Schröddinger differential equation system needed for time simulation of the quantum automaton is given. QuantumMaria, a software package for modeling and numerical simulation of quantum computers, is introduced.