Petri Net Modeling for Ising Model Formulation in Quantum Annealing

TL;DR

This paper introduces a Petri net modeling approach to systematically convert optimization problems into Ising models for quantum annealing, simplifying the formulation process.

Contribution

The paper proposes a novel Petri net-based method for formulating Ising models, making the process more straightforward and accessible.

Findings

Systematic extraction of constraints and objectives from Petri nets.

Conversion of Petri net models into binary quadratic nets.

Reduction in difficulty of Ising model formulation.

Abstract

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.