Modeling and Analysis of Margolus Quantum Cellular Automata Using Net-Theoretical Methods
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- Ojala L., Penttinen OM., Parviainen E. (2004) Modeling and Analysis of Margolus Quantum Cellular Automata Using Net-Theoretical Methods. In: Cortadella J., Reisig W. (eds) Applications and Theory of Petri Nets 2004. ICATPN 2004. Lecture Notes in Computer Science, vol 3099. Springer, Berlin, Heidelberg
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.
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