SoftBank and Tohoku University Develop Method to Streamline Quantum Computing Optimization

1. Introduction

SoftBank Corporation and Tohoku University have conducted joint research on the optimization of wireless communication environments using a quantum annealing computer. As a result, we have developed a method to efficiently reduce the number of variables※1 in mathematical equations required when solving combinatorial optimization problems※2. This method makes it possible to solve large-scale combinatorial optimization problems that could not be handled by quantum computers.

SoftBank is currently conducting research and development to improve the quality of wireless communications using quantum computers, and this joint research was conducted as part of that effort.

The results from this collaboration were presented at the Adiabatic Quantum Computing (AQC 2024) held in Glasgow, UK, June 10-14, 2024, and are expected to be published in an upcoming academic paper.

※1 Variables are the elements that determine what choices are made in a combinatorial optimization problem. In this wireless communication optimization, it refers to the combination pattern of wireless base stations and mobile terminals.

※2 A combinatorial optimization problem is the problem of finding the best combination of various alternatives to achieve a certain index (objective) under given constraints (conditions).

2. Background of the Joint Research

In wireless communication networks, the communication quality of each mobile device depends on the connection pattern of which mobile terminals are connected to which wireless base stations. For example, if a large number of mobile terminals are connected to a particular wireless base station and a small number of mobile terminals are connected to other wireless base stations, there will be areas where communication is comfortable and other areas where it is not. Therefore, optimizing the connection pattern between wireless base stations and mobile terminals will result in better overall communication quality.

Fig. 1. Images of connection patterns between wireless base stations and mobile terminals

However, as the number of wireless base stations and mobile terminals increases, the connection patterns increase exponentially. This makes it impractical to solve such combinatorial optimization problems within a reasonable timeframe using traditional classical computers. Consequently, while mobile network operators currently provide high-quality wireless communication within the limits of what can be calculated in practical timeframes, delivering even higher quality communication services will require more advanced approaches than those currently available.

Fig. 2. The number of connection patterns increases exponentially as the number of wireless base stations and mobile terminals increases(Case of 3 wireless base stations)

In recent years, quantum computers have gained attention as a new method for solving such problems in practical time. Specifically, annealing-based quantum computers are designed to tackle combinatorial optimization problems. Solving large-scale combinatorial optimization problems, such as the ones we face, requires a significant number of variables. However, the current annealing-based quantum computers are limited by the number of qubits they possess, which imposes restrictions on the number of wireless base stations and mobile devices that can be included in the calculations. Therefore, reducing the number of variables in the mathematical formulation of the problem has become a critical challenge.

Given this background, SoftBank and Tohoku University have developed a method to efficiently reduce variables in the mathematical formulation of combinatorial optimization problems using an annealing quantum computer (hereafter referred to as the "proposed method").

3. Details and Results of the Joint Research

In our joint research with Tohoku University, we conducted simulations using an annealing-based quantum computer to optimize connection patterns between multiple wireless base stations and a large number of mobile devices. The results demonstrated that by applying the proposed method for efficient variable reduction, it is possible to solve problems of a scale that traditional methods cannot handle. Furthermore, the connection patterns generated using our proposed method were found to deliver communication quality comparable to that achieved by conventional methods.

In this joint research, we focused on a combinatorial optimization problem aimed at maximizing the median DL-SINR* of all mobile devices within a given area where wireless base stations and mobile devices are distributed. The simulation validation was carried out using an annealing-based quantum computer. An example of the distribution pattern of wireless base stations and mobile terminals is shown in Figure 3. For the wireless base stations, we considered two scenarios: one with a single sector and one with three sectors. For the mobile devices, we examined two distribution scenarios: one where the devices are uniformly distributed and another where the devices are densely concentrated around specific wireless base stations. These variations were combined to create four distinct patterns for the analysis.

Fig. 3. An example of distribution pattern of wireless base stations and mobile terminals

※3 DL-SINR stands for DownLink Signal to Interference plus Noise Ratio. It is the ratio of the signal from a wireless base station received by a mobile terminal to the interference and noise affecting that signal. It is an indicator of how clearly data is being received.

As shown in Fig. 4, when solving a problem with a quantum computer, it is necessary to fit the variables within the number of qubits it has. However, when solving a large-scale problem with conventional methods, it is impossible to solve the problem because the variables used are larger than the number of qubits. By employing the proposed method, we can reduce the number of variables to a scale that can be managed by a quantum computer, thereby enabling the solution of previously unsolvable problems.

Fig. 4. Image of variable reduction

Fig. 5 shows how many variables (number of required qubits) are required for the conventional method and the proposed method when the number of mobile terminals is varied. For example, when optimizing the connection patterns between three base stations and 75 mobile terminals, the conventional method requires approximately 4,000 qubits. However, with the proposed method, the number of qubits used can be reduced to around 1,000, which is about one-fourth of the amount needed by conventional methods.

Fig. 5. Relation between the number of terminals and the number of qubits used in the conventional and proposed methods

Fig. 6 shows a graph comparing the accuracy of the proposed method with the conventional method for each distribution pattern in the case of 3 base stations and 30 mobile terminals. In this context, the "solution" refers to the median DL-SINR of all mobile devices within the area for each distribution pattern. The vertical axis represents the relative error compared to the exact solution, with lower values indicating a closer match to the exact solution. The graph clearly demonstrates that the proposed method yields results that are closer to the exact solution compared to the traditional method, indicating a higher accuracy in optimizing the connection patterns.

Fig. 6. Comparison of solution accuracy between conventional and proposed methods for each distribution pattern

4. Future Outlook

Through this joint research, we have successfully developed a method for efficiently reducing the number of variables, and the proposed method has been shown to produce results comparable to those of traditional methods. This achievement represents a significant milestone for SoftBank as we continue to explore the implementation of quantum computing across various business domains, including wireless communication.

Moving forward, SoftBank and Tohoku University will leverage the proposed method and insights gained from this joint research to further advance research and development aimed at improving wireless communication quality through the use of quantum computing.