Dec. 08, 2023

# Quantum Computational Research at the Frontier Research CenterPast and Future

The Frontier Research Center, Toyota Motor Corporation (hereafter Toyota) has been engaged in full-scale applied research using quantum computers since 2021. In this article, we would like to introduce the "past" and "future" of quantum computer research at the Frontier Research Center.

## Expectations for Quantum Computers

A quantum computer is a new type of computer that utilizes the principles of quantum mechanics. In a classical computer, the bits, the smallest unit of information, are in one of two states, "0" and "1," whereas in a quantum computer, a quantum bit (qubit) can be in not only "0" or "1" but also in a "superposition" of the two states. In other words, if there are N qubits, 2^{N} different conditions can be handled, so it may be able to speed up the computation.^{*1}

Classical computers have been improving their performance according to a rule known as Moore's Law, but there are concerns that their processing power is reaching a plateau. In addition, the amount of processing required of computing resources is increasing every year in response to the spread of IoT and the resulting increase in data volume, as well as increasingly complex services, systems, and social issues. Considering this background, expectations for quantum computers are growing more and more.

## My Encounter with Quantum Computer Research

As a collaborative system involving not only academia but also industry has been initiated for the social implementation of quantum computers, the Frontier Research Center has also started research utilizing quantum computers. Before explaining the details of the research, let me first briefly describe how I came to be involved in this study.

I had been engaged in the R&D of diesel engines for 10 years, specializing in computational fluid dynamics (CFD), but started engaging in work related to machine learning and optimization when I moved to the Frontier Research Center in 2016. In my new role at the Frontier Research Center, I was investigating the question, "How can we find better solutions faster?" and I became fascinated by the possibilities of quantum computers. It was also a time of increasing interest in quantum computer, and because seminars and voluntary study sessions were frequently held, I participated in them as much as possible as part of self-study, and I learned about quantum computer from the basics. Each year at Toyota, you are able to discuss your abilities and career plan with your supervisors. After sharing and discussing the possibility of quantum computer with my supervisors on such an occasion, I started engaging in quantum computer research in 2021.

## The Significance of Conducting Quantum Computer Research in Toyota

Though quantum computers have very high expectations, it is still difficult to apply them to real problems because both hard and soft systems are in development. On the other hand, quantum computing has had significant investments, and it is possible that technology can rapidly advance and solve problems faster than anticipated. As one of Toyota's divisions, the Frontier Research Center conducts research to create technologies to solve various social issues in the spirit of the Five Main Principles of Toyoda, "Stay ahead of the times."

- Figure 1 Formulating a real problem is also a challenge and where ingenuity comes in

As of 2023, it is not clear what problems will make quantum computers indispensable. In order to clarify this, it is necessary to accumulate verification cases using real data on various problems. Fortunately, Toyota has a wide variety of problems and data on them in various areas (design, manufacturing, logistics, human resources, etc.). By considering the use of quantum computers for those problems, we are able to determine the characteristics of problems in which they have strengths and weaknesses. We hope to contribute to the development of quantum technology and ultimately to the resolution of social issues by widely sharing the knowledge obtained from the results of these studies.

## The Study of Application to Optimization of Storage Arrangement in Parts Centers

In order to verify the capabilities of quantum computers and gather knowledge, we selected the quantum annealing machine (hereafter quantum annealer), which can handle relatively large-scale problems (large number of qubits) and has been the subject of active research for application. The primary use of quantum annealers is to solve combinatorial optimization problems. Combination optimization has been an issue in various areas within Toyota. For this research, the verification issue was how to optimize the storage arrangement of vehicle supply parts (hereafter parts) at a parts center, which is a difficult problem due to the huge number of combinations.^{*2}

This optimization problem is how to assign a wide variety of parts to storage shelves in a parts center. The worker walks to the storage rack when an order is placed, takes the parts around and returns (picking). There are several challenges in picking, but the objective of this verification was to reduce the distance traveled by workers. Figure 2 shows an image of reducing travel distance by changing the storage arrangement of parts. We will skip the detailed formulation,^{*3} but the distance traveled by the worker is expressed in the form of a quadratic unconstrained binary optimization^{*4} that can be handled by a quantum annealer, and a minimization problem is solved using it as the objective variable. In this article, we present an example of a problem with tens of thousands of variables solved by the so-called quantum-classical hybrid method,^{*5} which is used in conjunction with classical computers. Although tens of thousands of variables is quite small compared to a real problem, it should reflect the characteristics of a real problem as much as possible by applying the following innovations:

- Some excerpts from the actual shelf layout of the parts center
- Create pseudo-order data where the number of types of parts ordered at one time and the distribution of order frequency for each part match the actual order data, and the number of types of all parts in the pseudo-order data is arbitrarily selected.

- Figure 2 Reduction in worker travel distance by changing storage arrangement

A comparison with calculations using commercial optimization software on a classical computer (hereafter commercial software) showed that a 6-minute calculation using quantum-classical hybrid computation produced a solution that reduced the distance traveled by the worker compared to a 24-hour calculation using commercial software (Figure 3). The vertical axis of the graph shows the distance traveled per order, and although the difference between the two is only about three meters, for example, if one worker performs 100 picking operations per day and works 20 days per month, the distance traveled is reduced by 6 km per month. Thus, the results of this study demonstrate the potential of quantum computation technology.

- Figure 3 Computation time and average travel distance

## The Future of Quantum Computing Research at the Frontier Research Center

Toyota participates in the Council for the Creation of New Industries through Quantum Technology (Q-STAR) and the Quantum Innovation Initiative Council (QII), and is engaged in research and development of quantum technology through the exchange of information and joint research with research institutions and companies in industry, academia, and the government. Among them, the Frontier Research Center is an organization that conducts advanced research,^{*6} which is distinct from mobility development in its core business, and tackles various issues within the company without limiting the application of the technology. As mentioned earlier, we believe it is important now to accumulate verification cases in various situations without waiting for quantum computers to advance. Therefore, we are also working on validation for other issues than the optimization in the parts center described here. In addition to the verification of quantum annealers, we are also working on a gate-based quantum computer that can be used for general purposes.

Research in this field is making remarkable progress, and we need to accelerate the pace of our research. We are fortunate to have a number of researchers who are conducting cutting-edge research on quantum computers at Toyota Group companies nearby, and we are strengthening our collaboration with them by holding study sessions to discuss issues in the future mobility society and the use of quantum computers to address these issues. Quantum computer research may be a difficult challenge because there are many unknown areas, but it is because of this that allows researchers to come up with ideas and devise new ways of doing things. We will vigorously engage in research, believing that the solution to social issues lies ahead.

- Figure 4 Usual work (left) and team members (right; the author is in the center)

#### References

*1 | #Explaining Topic XX What is a Quantum Computer, AIST Magazine (Japanese only) |
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*2 | Billions of ways (see also, Case Studies of Research and Development in Logistics and Disaster Prevention and Mitigation by Mathematical and Data Scientists. Japanese subtitle data is included) |

*3 | For example, Applied Mathematics Volume 33, No. 3, p. 29, 2023 |

*4 | Also called QUBO (Quadratic Unconstrained Binary Optimization). An optimization problem in which the explanatory variables are binary variables, there are no constraints, and the objective variable is expressed in quadratic form. |

*5 | Using D-Wave Systems' quantum-classical hybrid solver service |

*6 | Throwing Light on Toyota's Plan B Design Group Toyota, Beyond Mobility, Toyota Times |

#### Author

Hiromitsu Kigure

Assistant Manager, Mathematical Engineering Research Group, R-Frontier Dept.

He has been involved in research and development of diesel engines using computational fluid dynamics (CFD), robust optimization and machine learning (natural language processing, time series prediction). He has been in charge of research on quantum computing technology since 2021.

#### Contact Information (about this article)

- Frontier Research Center
- frc_pr@mail.toyota.co.jp