Petri Net Modeling for Ising Model Formulation in Quantum Annealing
Round 1
Reviewer 1 Report
The paper proposes a Petri net modelling approach to the Ising model formulation for quantum annealing. The main advantage is related to the possibility of carrying out the process in a straightforward way if the target problem is known. The needed background is deeply described, but I think that it is widely merged with the contribution of the paper, making it not clear for readers. I prefer to concentrate the needed background in a single section and the proposal in a subsequent one. However, I think that the contribution is significant, so after a re-organization of the whole paper, it is can be considered as interesting for the acceptance.
Author Response
We appreciate the reviewer's valuable comments.
As the reviewer commented, readability should be improved, and to address this we modified the paper as follows:
We concentrated on the background in Section 2 and highlighted our contributions in Sections 3 and 4.
For more readability, we added a new subsection on ``Combinatorial Optimization Problems'' in Section 2, where we explain the basic definition of the problem and added an explanation to link it to Sections 3 and 4.
We also explained the quantum annealing process to enable readers to understand the research background in Section 2.2.
Moreover, we list the Petri net properties in Section 2.3 because they are used in Section 4.
Reviewer 2 Report
This manuscript proposed a novel Petri net modeling method for Ising model formulation for quantum annealing. Then, the proposed method was implemented using Python incorporated using well-known Petri net tools, CPNTools and SNAKES. The analysis results show that proposed method can drastically reduce the difficulty of the Ising model formulation. Overall, the topic of this study is interesting, and the manuscript was well organized and written. I suggest it can be considered to be accepted if the authors can well address the following comments.
- Please illustrate the main innovation of this research. Why was Petri net modeling selected for the task of interest? Why not other conventional methods?
- A flowchart is suggested to be added to explain the optimisation process.
- How can the authors avod the local optimum problem in optimisation.
- More future research should be added in conclusion part.
Author Response
We appreciate the reviewer's valuable comments.
Our answers to each comment are as follows:
For 1, a Petri net is an outstanding method for modeling target optimization problems because it can represent the structure and behavior of problem instances with simple rules; and the color and time extension provides powerful modeling capability.
Moreover, for the Ising model formulation, we can use various properties, extracted systematically from Petri net models.
These properties are well-defined in the Petri net theory.
We added this explanation in the conclusion to emphasize these important points.
For 2, we utilize the optimization mechanism provided in quantum annealing machines, such as D-waves.
To add to the context of our research, we have added a brief explanation of the quantum annealing process in Section 2.2.
For 3, quantum annealing is a metaheuristic and contains stochastic processes; therefore, local optima can occur.
Sensitive parameter tuning and careful annealing process control are required to maintain the quality of the solutions. However, this is not the topic of this paper. Therefore, we did not discuss this matter in this study.
For 4, We added more options for future research in the conclusion.
Reviewer 3 Report
This paper is well-written, both in terms of original contribution and readability. This paper focuses on the difficulty of formulating so-called "Ising and QUBO models," which is a valid problem to solve. The solution put forward in this paper is to formulate the problem as a Petri Net and then to map (generate) Ising or QUBO model. Since Petri Nets are easy to formulate, the authors' suggestions seem valid and interesting.
The paper presents all the issues (steps) that are involved in the process. For example, starting from the definition of Petri Nets, Ising and QUBO models, and Binary Quadratic Nets, the energy function, Minimum Vertex Cover, and Graph partitioning are also defined as preliminaries. Then, the mapping (construction or generation) of Petri nets into Ising models is presented. Finally, an application example is presented.
Though the original contribution seems worthy of publication, the authors evade a problem the practitioners may face: the sheer size of the Petri Nets for practical applications. The authors choose (purposely or otherwise) a simple problem as an application example, presenting it as part of the construction process. If the authors choose a real-life problem with the resulting huge Petri Net, it would reveal the difficulty of the transformation (from Petri Net to Ising model). Nevertheless, this reviewer believes that the originality and the idea presented in this paper are worthy of publication.
Author Response
We appreciate the reviewer's valuable comments.
Exactly, we faced the problem the reviewer pointed out, and we are now attacking this with real-life applications.
We believe that we can answer this problem with some case studies in the near future.
Round 2
Reviewer 1 Report
I appreciate the effort spent by the authors to improve the paper. No further comments.
