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International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC)

Modeling of Quantum Computer by using Quantum Petri Net

Ito Shinsuke, Atsushi Ohta, Kohkichi Tsuji

Published Jul 1, 2008• 3 citations
OpenAlex

Abstract

Petri Net that is an effective tool for concurrent systems, has been extended to Quantum Petri Net. The conventional modeling method of quantum computer using Quantum Petri Net, have several drawbacks. This paper defines new model and examines conditions to solve these drawbacks, and proposes new model from modeling quantum Turing machine, and shows that the model can simulate more general calculation processes than which the conventional model.

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Petri Net that is an effective tool for concurrent systems, has been extended to Quantum Petri Net. The conventional modeling method of quantum computer using Quantum Petri Net, have several drawbacks. This paper defines new model and examines conditions to solve these drawbacks, and proposes new model from modeling quantum Turing machine, and shows that the model can simulate more general calculation processes than which the conventional model.
The development of quantum software applications requires models capable to describe quantum features (superposition, entanglement, reversibility etc.) as well as the software algorithm requirements. The newly proposed Quantum Petri Nets (QPNs) have the structure of the classical Petri Nets (PNs), but their tokens represent superposed quantum states fulfilling the Hilbert space features. Instead of the integer numerical values of the PN marking, QPNs use quantum marking describing an extreme huge space. New conditions for the transition enabling and new mappings for the transition executions are conceived. A PN based language is used for the structure analysis. Replacing the classical tokens with the probability distribution of the quantum vectors, the QPN simulation is possible as well as the construction of a reachability graph.
Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas of everyday life. Our research is aimed at the proposal of a Petri net modeling approach for an Ising model formulation. Although the proposed method requires users to model their optimization problems with Petri nets, this process can be carried out in a relatively straightforward manner if we know the target problem and the simple Petri net modeling rules. With our method, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models, extracted systematically from Petri net models, and then converted into binary quadratic nets, equivalent to Ising models. The proposed method can drastically reduce the difficulty of the Ising model formulation.
Classical Petri nets provide a canonical model of concurrency, with unfolding semantics linking nets, occurrence nets, and event structures. No comparable framework exists for quantum concurrency: existing ''quantum Petri nets'' lack rigorous concurrent and sound quantum semantics, analysis tools, and unfolding theory. We introduce Quantum Petri Nets (QPNs), Petri nets equipped with a quantum valuation compatible with the quantum event structure semantics of Clairambault, De Visme, and Winskel (2019). Our contributions are: (i) a local definition of Quantum Occurrence Nets (LQONs) compatible with quantum event structures, (ii) a construction of QPNs with a well-defined unfolding semantics, (iii) a compositional framework for QPNs. This establishes a semantically well grounded model of quantum concurrency, bridging Petri net theory and quantum programming.