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

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

Fortunately, a research team from the Tokyo University of Science in Japan is working to find solutions to this problem with Ising machines. In a recent study led by Professor Takayuki Kawahara, they reported an innovative method capable of halving the number of interactions requiring physical implementation. Their findings were published in the journal IEEE Access on October 1, 2024.

The proposed method focuses on visualizing the interactions between spins in the form of a two-dimensional matrix, where each element represents the interaction between two specific spins. Since these interactions are “symmetric” (i.e. 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 existed for several years. years. In 2020, Professor Kawahara and colleagues presented a method for folding and rearranging the remaining half of the rectangle-shaped interaction matrix to minimize the circuit footprint. Although this led to efficient parallel calculations, the wiring required to read interactions and update spin values ​​became more complex and harder to scale.

In this study, researchers proposed a different way to halve the interaction matrix, which leads to better circuit scalability. They divided the matrix into four sections and halved each of these sections individually, alternately preserving the “top” or “bottom” halves of each sub-matrix. Then, they folded and rearranged the remaining elements into a rectangular shape, unlike the previous approach, which retained the regularity of its arrangement.

Taking advantage of 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 rounds on just eight FPGA chips. In other words, two independent and fully connected Ising machines could be implemented on the same board.“, notes Professor Kawahara, “Using these machines, two classic combinatorial optimization problems were solved simultaneously, namely the maximum cut problem and the four-color problem.»

The performance of the circuit developed for this demo was astonishing, especially when compared to the slowness of a conventional computer in the same situation. “We found that the performance ratio of two independent, fully coupled 384-round Ising machines was approximately 400 times higher than that of simulating one Ising machine on a standard Core i7-4790 CPU to solve the two problems sequentially.», reports Kawahara, enthusiastic about the results.

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

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Reference

DOÏ: 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 Hokkaido. Founded in 1881, the university has continually contributed to Japan’s scientific development by instilling a love of science among researchers, technicians and educators.

With the 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 sciences to applied sciences. TUS has adopted a multidisciplinary approach to research and has undertaken intensive studies in some of today’s most vital areas. TUS is a meritocracy where the best in science is recognized and encouraged. It is the only private university in Japan that has produced a Nobel Prize winner and the only private university in Asia to produce Nobel Prize winners. the field of natural sciences.

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About Professor Takayuki Kawahara from Tokyo University of Science
Dr. Takayuki Kawahara is a professor in the Department of Electrical Engineering, Tokyo University of Science, Japan. He received his Ph.D. He received his PhD from Kyushu University in 1993. With over 8,500 citations, Professor Kawahara’s current research is dedicated to sustainable electronics, with a particular focus on low-power AI devices and circuits , sensors, spin current applications and quantum computing techniques. It has won several awards, including the IEICE Electronics Society Award 2014 and the Science and Technology Award (Development Category) in 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 Grants 22H01559 and 23K22829.