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A 48-node graph with 90% connected edges. The diagram shows the complexity of the architecture that connects everything. Credit: Lo et al.

Quantum computers, systems that perform calculations by exploiting quantum mechanics phenomena, can help to efficiently deal with many complex tasks, including so-called integration problems. These are problems that involve identifying the best combination of variables among multiple choices and under a set of constraints.

Quantum computers that can deal with these problems must be based on reliable hardware systems, with complex connections of all nodes. This connection ultimately allows graphs representing arbitrary dimensions of the problem to be plotted directly on computer hardware.

Researchers at the University of Minnesota recently developed a new electronic device based on conventional metal oxide semiconductor (CMOS) technology that can support this critical mapping process. This tool, introduced on the page at *Natural Electronics*is a physics-based Ising solver consisting of coupled ring oscillators and an all-to-all node coupled design.

“Building interconnected hardware where each node (ie, oscillator) can ‘talk’ to all other nodes is very difficult; as the number of connected nodes (N) increases, the number of connections per node increases by ~N^{2}. This leads to increased voltage and more hardware at each point that makes the connection less efficient and more balanced,” Chris Kim, one of the researchers who conducted the study, told Phys.org.

“Previous works, including ours, have focused on locally connected structures where each site can communicate with only a few individuals (for example, the Ising solver by Kim and his colleagues has a complete design consisting of 48 spins and parallel coupling. The horizontal oscillator in the device is coupled close to the vertical oscillators, they form horizontal-vertical oscillator pairs that combine with other pairs to form a crossbar array.

“The basic idea behind our Ising solver is to propagate the signal in both horizontal and vertical directions in such a way that node i and node j meet each other in the cross-bar array,” explained Kim. “By placing a coupler circuit at each intersection, we can build a series of circuits in which the signal of each node speaks to all the other signals of the node. Although the oscillating signals are changed in phase throughout the series, the connection between the two nodes occurs in such a way that the phases are changed that is why the proposed design achieves a competitive solution.”

The researchers tested their Ising target in a series of tests, where they used it to perform various mathematical operations, collect measurements for problems of different sizes and different graph densities. Their results were promising, as graphs representing the dimensions of these problems could be drawn effectively on their chip.

“With our new method, we can directly map the problem graph to up to 48 nodes in the solver,” Kim said. “This is a significant improvement over previous designs; for example, King’s graph-based hardware was exposed to multiple nodes including ours, but each node could only talk to eight other neighbors.”

In the future, the chip introduced by Kim and his colleagues could inform the design of more Ising solvers and devices that can display complex problem graphs. This could ultimately help improve the ability of quantum computers to solve complex problems, facilitating real-world deployments.

“Since the problems we want to solve are much larger than a single hardware model, we need to find a way to decompose and iterate the problems without sacrificing the accuracy of the solution,” added Kim.

“Another interesting topic is comparing the quality of our hardware solution against existing optimization algorithms such as simulated annealing or tabu search. Finally, we will have to find systematic ways to formulate the problem in combining complexity; we cannot democratize this computational method if a human expert is needed at every step of the calculation.”

**More information:**

Hao Lo et al, An Ising solver chip based on a coupled ring oscillator with a 48-node all-in-one integrated architecture, *Natural Electronics* (2023). DOI: 10.1038/s41928-023-01021-y

**Journal information:**

Natural Electronics

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