Computers are essential for solving complex problems in areas such as scheduling, logistics, and route planning, but traditional computers struggle with large-scale combinatorial optimization because they cannot efficiently process large numbers of possibilities. To solve this, researchers have explored specialized systems.

One such system is the Hopfield network, a significant breakthrough in artificial intelligence since 1982, proven in 1985 to solve combinatorial optimization by representing solutions as energy levels and naturally finding the lowest energy or optimal solution. Based on similar ideas, Ising machines use the principles of magnetic spin to find efficient solutions by minimizing the energy of the system through a process similar to annealing. However, a major challenge of Ising machines is their large circuit footprint, especially in fully connected systems where each spin interacts with others, complicating their scalability.

Fortunately, a research team at the University of Science in Tokyo, Japan, has been working to find solutions to this problem with Ising machines. In a recent study led by Professor Takayuki Kawahara, they reported an innovative method that can halve the number of interactions that need to be physically implemented. Their findings were published in the journal Access IEEE on October 1, 2024.

The proposed method focuses on visualizing the interactions between wheels as a two-dimensional matrix, where each element represents the interaction between two specific wheels. Because these interactions are “symmetric” (ie, the interaction between Spin 1 and Spin 2 is the same as that between Spin 2 and Spin 1), half of the interaction matrix is ​​redundant and can be omitted – this concept has been around for many years. In 2020, Prof. Kawahara and colleagues presented a method of folding and rearranging the remaining half of the interaction matrix into a rectangular shape to minimize the circuit footprint. While this led to efficient parallel computations, the wiring required to read the interactions and update the spin values ​​became more complex and difficult to scale.

In this study, the researchers proposed a different way of halving the interaction matrix that leads to better circuit scalability. They divided the array into four sections and halved each of these sections individually, alternately keeping either the “upper” or “lower” halves of each subarray. They then folded and rearranged the remaining elements into a rectangular shape, unlike the previous approach, which preserved the regularity of its arrangement.

Using this crucial detail, the researchers implemented a fully coupled Ising machine based on this technique on their previously developed custom circuit containing 16 field-programmable gate arrays (FPGAs). “Using the proposed approach, we were able to implement 384 spins on just eight FPGA chips. In other words, two independent and fully connected Ising machines could be implemented on the same board,” notes Prof. Kawahara, “Using these machines, two classic combinatorial optimization problems—namely, the maximum-cut problem and the four-color problem—were solved simultaneously.”

The performance of the circuit developed for this demonstration was astounding, especially compared to how slow a conventional computer would be in the same situation. “We found that the performance ratio of two independent Ising machines with 384 spins fully coupled was about 400 times better than simulating an Ising machine on a regular Core i7-4790 processor to solve the two problems sequentially”, reports Kawahara, delighted with the results.

In the future, these cutting-edge developments will pave the way to scalable Ising machines suitable for real-world applications, such as faster molecular simulations to accelerate drug and materials discovery. In addition, improving data center and power grid efficiency is also feasible for use cases that align well with global sustainability goals of reducing the carbon footprint of emerging technologies such as electric vehicles and 5G/6G telecommunications. As innovations continue to develop, scalable Ising machines may soon become invaluable tools across industries, transforming the way we approach some of the world’s most complex optimization challenges.

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Reference

TWO: 10.1109/ACCESS.2024.3471695

About Tokyo University of Science
Tokyo University of Science (TUS) is a well-known and respected university and the largest private research university specializing in science in Japan, with four campuses in central Tokyo and its suburbs and in Hokkaido. Established in 1881, the university has continuously contributed to the development of Japan’s science by instilling a love of science in researchers, technicians and educators.

With a mission of “Creating science and technology for the harmonious development of nature, human beings and society”, TUS has undertaken a wide range of research from basic science to applied science. TUS has embraced a multidisciplinary approach to research and has undertaken intensive studies in some of today’s most vital fields TUS is a meritocracy where the best of science is recognized and cultivated. It is the only private university in Japan to produce a Nobel Prize winner and the only private university in Asia to produce Nobel Prize laureates. the field of natural sciences.

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About Professor Takayuki Kawahara of Tokyo University of Science
Dr.Takayuki Kawahara is a professor in the Department of Electrical Engineering at Tokyo University of Science, Japan. He earned his Ph.D. from Kyushu University in 1993. With over 8,500 citations, the current research of Prof. Kawahara are dedicated to sustainable electronics, with a special focus on low-power AI devices and circuits, sensors, spin current applications, and quantum computing techniques. He has won several awards, including the 2014 IEICE Electronics Society Award and the Science and Technology Award (Development category) at the FY2017 Science and Technology Commendation by the Minister of Education, Culture, Sports, Science and Technology of Japan.

Funding information
This work was supported in part by the Japan Society for the Promotion of Science (JSPS) KAKENHI under Grant 22H01559 and Grant 23K22829.