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# Quantum code developed at Purdue University could tackle problems from semiconductors to commodities

WEST LAFAYETTE, Ind. — A unique library of computer code, built on equations derived for quantum mechanics, could be used to model problems as diverse as the flow of electrons through a nanoscale device or the price of copper in a commodities market. Begun more than a decade ago through the Nanoelectronic Modeling Group at Purdue University, elements of the library are today used by Intel for advanced transistor designs, while the most current version is available for commercial licensing through Silvaco Inc., or free to academics through the Purdue Research Foundation.

The core capabilities of the NanoElectron MOdeling Tool suite, known in its fifth iteration as NEMO5, are highly specialized atomic-resolution calculations of nanostructure properties – strain relations, phonon modes, electronic structure, self-consistent Schrödinger-Poisson calculations, and quantum transport. But don't let the quantum-scale concepts deter you. While the math is complex, the concept is as familiar as a pebble tossed into a quiet pond.

"What we're really solving are wave equations," said Tillmann Kubis, a research assistant professor in the Elmore Family School of Electrical and Computer Engineering, and developer of the NEMO5 suite. "These equations describe resonances from fundamental entities –an electron, a proton, a muon and so forth— but in the end, it's just waves. People think it's counter-intuitive, but any child can get the experience of wave equations by throwing stones into a pond and watching what happens to the waves."

At present, the NEMO5 tool suite is primarily applied to solid state physics problems, with sections of code used by major players in the semiconductor industry – Intel, TSMC, Global Foundries – to model myriad devices including logic devices, sensors and light-emitting diodes. But Kubis is expanding that domain by working with mechanical engineers interested in heat transport and chemical engineers to model chemical reactions. He even presented to the U.S. Air Force a concept for modeling the movement of swarm drones under attack.

"For the semiconductor field, NEMO5 has paid dividends in a very significant way. But I really want to implement it for disciplines that people would never consider," Kubis said, "whether it's swarms of drones, neurons, or commodities. That's my long-term vision."

The quantum (or wave) equations encoded in the NEMO5 tool suite envision reality as a symphony of resonances – emanating from subatomic particles that are converging, crashing and diminishing over distance into oblivion. And while these equations were created to explore quantum phenomena, there are many more familiar interactions – the spread of a virus, neurons firing in a pattern of thought, rush hour traffic surging from a city center – that could also be described with the mathematics of waves.

"Systems that basically have infinite degrees of freedom, or very high complexity, this is what we have been handling for semiconductor giants for decades," Kubis said. "And we have very good means to reliably predict how that stuff happens."

Many of these systems are currently studied by network scientists, but as Kubis points out, the links and nodes of a network – a neural network, a social network, people in a pandemic, animals in a food web – are just the infrastructure. The movement of energy, ideas, viruses and life within that infrastructure can be modeled "more accurately, elegantly and efficiently" with many-particle wave equations.

In a simplified example, to model the movement of a stadium wave you could use a supercomputer and individually simulate each of the 80,000 spectators; predicting when they realize a wave is approaching, when they stand, when they sit. Or you could measure the speed of the wave as it moves around the stadium, an equally accurate but far less computationally intense method.

Kubis has seen the success of this translation with the code he built for Intel. One module of code, which runs on a supercomputer, simulated as many as 1 million individual atoms in exquisite detail. But another module simulates collective resonances, providing nearly identical results for a tiny fraction of the computational cost.

"If it's a complicated system, with lots of unknowns, lots of degrees of freedom, it could even be impossible to solve with calculations based on the behavior of individual entities. But what's really going on is that a wave is propagating through entities. And then it's simple, it's just a wave."

The interactions of a system that can be modeled on the NEMO5 tool suite need only adhere to two criteria: the system is composed of many indistinguishable entities (people, neurons, cars); and the entities must be interacting, but in a limited range (a city, a brain, an arterial highway line). These are the criteria of particle physics, and while the NEMO5 tool suite is built on those equations, the computer code is deliberately modular and nonfield specific, enabling it to tackle problems beyond the quantum scale.

"NEMO5 is a toolbox for many-particle problems. But no one says many-particle physics is limited to small things. It could be for any system with indistinguishable entities interacting in a limited range," Kubis said. "The quantum code library takes these sophisticated wave equations and hacks them into code snippets that solve equations, but the equations don't care whether they're solving for electrons or people."

The NEMO5 tool suite has been developed with support from the National Science Foundation, the Semiconductor Research Corp., and Intel. It can be licensed academically through the Purdue Office of Technology Commercialization and commercially licensed via Silvaco Inc.