# Ising’s physics-based solution is based on standard CMOS technology

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A 48-node graph with 90% of the edges connected. The figure shows the complexity of the overall connected architecture. Credit: Lu et al.

Quantum computers, systems that perform computations by exploiting quantum mechanical phenomena, can help efficiently address many complex tasks, including so-called combinatorial optimization problems. These are problems that entail determining the optimal set of variables from among several options and under a series of constraints.

Quantum computers that can address these problems must rely on reliable hardware systems, which have complex all-to-all nodal communication. This connection eventually makes it possible to map graphs representing arbitrary dimensions of the problem directly onto computers.

Researchers at the University of Minnesota recently developed a new electronic device based on standard complementary metal oxide semiconductor (CMOS) technology that can support this crucial mapping process. This device was presented in a paper in *Nature electronics*is a physics-based Ising solution consisting of coupled toroidal oscillators and a structure connected to the global node.

“Building an all-to-all connected device where each node (i.e. oscillator) can ‘talk’ to all other nodes is very difficult; as the number of paired nodes (N) increases, the number of connections per node increases by ~N^{2}. “This increases the electrical load and hardware overload of each node quadratically, making the coupling less efficient and less uniform,” Chris Kim, one of the researchers who conducted the study, told Phys.org.

“Previous work, including ours, focused on a locally connected architecture where each node can talk to only a few (e.g., <10) nearby nodes. A global architecture is ideal where issues can be mapped directly to hardware but up to this point "There was no elegant way to achieve this."

The Ising solution devised by Kim and colleagues has an overall structure with 48 turns and a highly uniform coupling circuit. The horizontal oscillator in the device is closely coupled to the vertical oscillators, creating pairs of horizontal-vertical oscillators that intersect with other pairs to form a cross-array.

“The basic idea behind our Ising solution is to propagate an oscillating signal in both the horizontal and vertical directions in such a way that node i and node j intersect each other across the crossbar array,” Kim explained. “By placing a coupler circuit at each junction, we can build a circuit array where each node’s signal talks to all the other nodes’ signals. Even though the oscillating signals are shifted throughout the array, coupling between two nodes occurs in such a way that they account for variable phases and that’s why In that the proposed design finds a competitive solution.”

The researchers evaluated their Ising tool in a series of tests, using it to perform different statistical operations, collecting measurements for problems of different sizes and different data densities. Their results were promising, as graphs representing the dimensions of these problems could be effectively drawn on their chips.

“With our new approach, we can directly map the problem graph with up to 48 solver nodes,” Kim said. “This is a huge improvement over previous designs; for example, graph-based King devices have been demonstrated by several groups including ours, but each node can only talk to eight other neighbors.”

In the future, the chip presented by Kim and his colleagues could help create more Ising solvers and devices that can draw complex graphs for problems. This could ultimately help improve the ability of quantum computers to solve combinatorial optimization problems, making them easier to deploy in the real world.

“Since the problems we want to solve are much larger than a single device instance, we will have to find a way to decompose and reconstruct sub-problems without sacrificing the accuracy of the solution,” Kim added.

“Another interesting topic is to compare the quality of our hardware solution with existing optimization algorithms such as simulated annealing or search toboost. Finally, we will have to find more systematic ways to formulate the weight coupling problem; we cannot democratize this computing approach if a human expert in Every step of the calculation.

**more information:**

Hao Lo et al., an Ising solver chip based on coupled toroidal oscillators with a global connected matrix structure of 48 nodes, *Nature electronics* (2023). doi: 10.1038/s41928-023-01021-y

**Magazine information:**

Nature electronics

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