Combinatorial optimization problems are omnipresent. We might not think about it, but in our daily lives we often deal with challenges that can be resolved in myriad ways.

“A feature common to combinatorial optimization problems is that they quickly become impossible to solve as the number of parts to be optimized grows, and the number of potential solutions grows exponentially. A simple example occurs when preparing for a journey. Cases need to be packed in the car to make best use of the space available. But cases come in different shapes and sizes that must be packed into a limited space, which can be done in innumerable combinations,” says Åkerman, who is a professor of experimental physics at the University of Gothenburg.

In society there are many combinatorial optimization problems, in areas such as encryption, resource allocation, business planning and timetabling.

“Which patients should be put where in a hospital? How do we optimize the electricity grid and cross-border power transfer capacity? How can we rationalize elevator movements in a hotel? Combinatorial optimization problems occur on greater and lesser scales, and we solve them reasonably well – perhaps up to 80 percent. But when we try to solve them really well and really quickly, we are currently not very successful,” he says.

Efficient calculations using oscillators

Åkerman has his sights set on solving combinatorial optimization problems using large networks of oscillators. Oscillators may be described as electronic circuits that produce a periodic, oscillating or alternating current. They can make advanced calculations – roughly in the way our neurons do.

Over the past ten years Åkerman has established world-leading research in this field.

The funding I’ve received from the Foundation gives me a security and stability that is absolutely invaluable for a researcher.

“If we can solve combinatorial optimization problems efficiently, society will get more out of existing resources, and reduce all the ‘waste’ that occurs because we don’t do things in the right way. Accessing almost 20 percent more resources would have a huge impact in many areas, but even lower increases would make a big difference. Imagine, for example, if we could improve traffic flow by five percent and get rid of many traffic jams, or if we could achieve ten percent more rail traffic on the railroad network and reduce the number of delays,” he says.

Networks striving for the perfect state

Strenuous research efforts are currently being made to build quantum computers capable of performing ultrafast advanced computations. But usable quantum computers remain difficult and costly to make, and their use requires large amounts of energy.

Åkerman’s research focuses on building “Ising machines.” These are large networks of alternating nano-oscillators capable of performing huge numbers of computations extremely quickly and energy-efficiently.

The oscillators in the networks are connected to each other and interact constantly with their neighbors. The researchers vary the strength of the connections, enabling them to program different combinatorial problems. The oscillators respond by altering their phase state so they are in-phase or anti-phase, together endeavoring to achieve the perfect state, where all oscillators are optimally connected to each other.

“The oscillators vibrate and their phase fluctuates until the system finds its best collective state – i.e. the solution to the combinatorial problem. The challenge is to create and program really large networks so the oscillators can solve significant problems, such as the distance between cities in order to find the shortest route, for example,” says Åkerman. He elaborates:

“If we can solve combinatorial optimization problems quickly and energy-efficiently, it may open up possibilities that we haven’t even thought of yet.”

Paving the way for more efficient technology

In a few years’ time Åkerman hopes to have created a commercially viable Ising machine. And he’s already well on the way. So far the research team has managed to connect up a network of 100,000 synchronized oscillators in a very small space.

“The oscillators measure only ten nanometers* and are placed 24 nanometers from each other in a matrix. Currently this makes it possible to fit 1.7 billion oscillators on a one-square-millimeter chip,” he explains.

These minute formats offer great potential for more efficient technology, especially in smaller applications such as drones or mobile phones.

“Small chips with energy-efficient computation abilities would facilitate numerous mobile phone functions,” he says.

The world of electronics has appealed to Åkerman for as long as he can remember. As a teenager he busied himself with his ABC 80 computer and built his own electric organ. He has always been driven by a desire to understand and explain how the world works, and also to control processes and phenomena.

“Deep down I’m an engineer, and engineers like to create things. I’ve started a number of research-based companies, so as well as being a researcher, I’m an entrepreneur,” he says.

Text Ulrika Ernström
Translation Maxwell Arding
Photo Johan Wingborg