A 48-node graph with 90% of the edges connected exemplifies the intricate nature of an all-to-all connected architecture, as credited to Lo et al.
Quantum computing, which harnesses the principles of quantum mechanics, holds promise for efficiently addressing complex tasks, particularly combinatorial optimization problems. These problems involve identifying the optimal combination of variables within a set of constraints and options.
The effectiveness of quantum computers in handling these challenges hinges on the reliability of their hardware systems, particularly those featuring a sophisticated all-to-all node connectivity. Such connectivity enables the direct mapping of problem dimensions onto the computer hardware.
Recently, researchers from the University of Minnesota unveiled a groundbreaking electronic device built on standard complementary metal oxide semiconductor (CMOS) technology, specifically designed to support this critical mapping process. Described in a paper published in Nature Electronics, this device serves as a physics-based Ising solver. It is composed of coupled ring oscillators and an all-to-all node connected architecture.
Chris Kim, one of the researchers involved in the study, acknowledged the formidable task of constructing hardware with all-to-all connectivity. As the number of coupled nodes (N) increases, the number of connections per node grows quadratically (~N^2), resulting in escalating electrical loading and hardware overhead. This makes the coupling less efficient and uniform.
Kim stated, “Previous works, including our own, focused on locally connected architectures, where each node could communicate with only a limited number of nearby nodes (e.g., <10). An all-to-all architecture is ideal for direct hardware mapping, but until now, an elegant solution remained elusive." The Ising solver developed by Kim and his team features an all-to-all architecture comprising 48 spins and a highly uniform coupling circuit. Horizontal oscillators closely interact with vertical oscillators, forming pairs of horizontal-vertical oscillators that intersect with other pairs to create a crossbar array. Kim explained the core concept behind their Ising solver, involving the propagation of oscillating signals in both horizontal and vertical directions, ensuring that each node interacts with every other node throughout the crossbar array. Coupler circuits at these intersections enable signal communication between all nodes, despite phase shifts, enabling the proposed design to yield competitive solutions. The researchers conducted extensive testing of their Ising solver, employing it for various statistical operations across problems of varying sizes and graph densities. Their results were promising, demonstrating effective mapping of problem dimensions onto their chip. Kim stated, "With our new approach, we can directly map a problem graph with up to 48 nodes onto the solver hardware. This is a significant improvement over previous designs; for instance, a King's graph-based hardware, demonstrated by several groups, including ours, allowed each node to communicate with only eight neighbors." In the future, the chip developed by Kim and his colleagues may pave the way for the creation of more Ising solvers and devices capable of mapping complex problem graphs. This advancement could further enhance the ability of quantum computers to solve combinatorial optimization problems, facilitating their practical application. Kim concluded by highlighting the need to decompose and recompose sub-problems without sacrificing solution accuracy for larger problems. Additionally, there is a need to compare the solution quality of their hardware against existing optimization algorithms and develop more systematic approaches to formulate problem-to-coupling weights, ultimately democratizing this computing approach.