Machines that will provide the best solution to difficult problems  

Johan Åkerman will asa Wallenberg Scholar build Ising machines to solve problems with a huge number of parameters and possibilities, known as combinatorial optimisation problems.

The travelling salesman problem is a classic optimisation problem that involves finding the shortest route for a travelling salesman between a number of different cities. The problem is a so-called combinatorial optimisation problem that is characterised by the fact that it very quickly becomes impossible to solve when the number of parts to be optimised increases. A salesman who wants to visit 5 cities can do so in 12 different ways, but if he wants to visit 21 cities, there are 10¹⁸ different ways to do so. If it takes one second to measure the length of one such distance, even the age of the universe would not be enough to go through all of them.

Breaking encryption

Another equally difficult problem is finding the prime factors of very large integers, which is the basis of all public encryption protocols. Encryption can be broken if you can find out what the prime numbers are.
Today, enormous resources are spent on quantum computers to solve such combinatorial optimisation problems, but building a useful quantum computer is still very difficult.

“Therefore, I and other researchers have looked into computing with physical systems that exploit their inherent parallel properties. Networks of interacting oscillators can solve a wide range of combinatorial optimisation problems as efficiently as quantum computers,” says Johan Åkerman, Professor of Experimental Physics at the Department of Physics at the University of Gothenburg.

Two different Ising machines

In these networks, called Ising machines for historical reasons, all oscillators interact with each other and synchronise with their neighbours either in phase or in antiphase. By controlling whether their coupling is in phase or out of phase, and by controlling how strongly the different oscillators couple to each other, the network will try to find the state in which all oscillators couple as optimally as possible to their neighbours. The final state is precisely the solution to the combinatorial problem defined by the different coupling strengths.

Johan Åkerman wants to use two different ways to build Ising machines. The first machine is based on his world-leading research on large networks of spin-Hall nano-oscillators. The second is based on the researchers' recent findings on how spin-wave pulses can serve as building blocks for an Ising machine. The research team then studies the Ising machines with two unique spin-wave microscopes that can measure the individual state of each node in the Ising machine. 

“These two Ising machines can become much more powerful. We hope to give Sweden a leading position in the new computing technology,” says Johan Åkerman.