Work by Eun-Ah Kim, an Illinois Physics alumna and professor at Cornell University, helps prove the feasibility of using non-Abelian anyons in quantum computing.
Alumna Eun-ah Kim: ‘At the brink in quantum computing’
Bill Bell
for Illinois Physics
Professor Eun-Ah Kim has been keeping her eye on anyons for more than two decades. While completing her doctoral degree with Illinois Physics Professor Eduardo Fradkin in the early 2000s, she explored how anyons “see” each other. Like other quasiparticles, anyons are collections of fundamental subatomic particles that can be grouped and treated as a single particle. However, unlike fundamental particles, exchanging positions between a pair of anyons changes the state of the whole system.
“Anyons are a very intriguing notion,” explains Kim, who is a professor at Cornell University. “There isn’t anything that more dramatically speaks to the fact that when many bodies interact, something totally new can happen.”
“Something totally new” can have very useful applications in quantum computing. Groups of anyons, for example, can serve as a qubit—the quantum-mechanical entity used as the basic unit of calculation in quantum computing.
The problem is that something totally new only happens under very particular circumstances that are difficult to create.
“I was always interested in seeing beautiful ideas manifested in the lab,” says Kim. But during her doctoral studies, “how hard the experiments were going to be was beyond my grasp. And beyond the field at the time. It started to dawn on me, and to the field, that these things are very difficult to control to the degree you want to control. We started to do the engineering to build experiments that could capture the behavior of anyons and overestimated how much we could do at the time.”
According to Kim, the time now seems to have come. “We appear to be at the brink of the control we need.”
Kim, then-postdoctoral researcher Dr. Yuri Lensky, and colleagues at Google published a pair of papers in 2023. The first outlined a theoretical framework for using bulk anyons to encode a logical qubit and braid them to do a gate operation (that is, the switching from one state to another that is the basis for all digital and quantum computing). The second, published in Nature, implemented that protocol using what are known as non-Abelian Ising anyons for the first time.
After more than 20 years, this incredibly fruitful collaboration came together fast for Kim.
“From the outside view, it might have appeared I had moved on. But it is close to my heart, my first love. I was waiting for the right opportunity. Any time it seemed like something might work—a new type of superconductor or topological insulator or a new platform—I would look at it and write a paper on it. But I was never convinced I would see braiding in the immediate future on any of the previous platforms,” she says.
That changed when the leader of Google’s Quantum AI efforts, Dr. Pedram Roushan, presented at Cornell in February 2022. The team was touting their development of a quantum processor based on superconducting qubits that could move and braid Abelian anyons. Thus, they could begin to verify long-established theoretical predictions about how the anyons behaved.
Kim believed that the processor could be used to encode a logical state non-locally among non-Abelian anyons and change the quasiparticles’ logical state by braiding them. By May, Lensky had developed a proposal for how to do that work and was in Santa Barbara pitching the idea to Google Quantum AI.
“He developed a roadmap for how to make this all happen,” says Kim. “He went there thinking that this would probably be too hard. But he talked to the experimentalists and came back so energized. ‘Eun-Ah, this can be done!’”
Lensky and Kim then began implementing the experiment with a large team from the company. They released their successful results on arXiv.org in October 2022, and the journal articles were published in May 2023. Lensky has since gone to work at Google Quantum AI. Kim and her team continue to investigate the space as well, including the one additional logical gate that would be needed to build a fully functional universal quantum computer from non-Abelian anyons.
Kim says the experiments embodied her early work with doctoral advisor Eduardo Fradkin, despite the fact that “Eduardo is on the other end of the spectrum from engineering.” His influential work in lattice gauge theory was central to the approach Lensky took to his “experimental playbook” for non-Abelian anyon braiding, especially in the efficient and robust protocols for moving anyons. Because of inherent noise and decoherence, the efficiency of the move was critical for reaching the intended outcome.
“We are trying to manipulate a very complex wave function by manipulating each physical qubit,” Kim explains. “Each time we do something to a qubit, we are giving it time to decohere. The quality deteriorates with time. If we wanted to see what we were envisioning, we needed a robust and efficient way to get to the goalpost. Thinking about it from a gauge-theory perspective allowed Yuri to invent a protocol that was explicitly efficient and robust.”
The work was also a terrific example of one of the reasons Kim became a teacher and mentor like Fradkin. Seeing Lensky return from his first visit to Google so excited “was pivotal for me in my career,” says Kim. “I became more hopeful than ever that this dream of anyonic braiding done predictably can possibly come true. But it was also the moment of witnessing non-linear growth in a young person.
“Yuri became a different person after that visit. That’s the reward of being in academia. Seeing talented young people and trying to find ways for their potential to burst. When I manage to help make that happen, it is so rewarding. I have always known that Yuri is really brilliant. But the world can only see results. He was able to connect that brilliance—what is really special about him—to an obviously valuable outcome. And that’s what it takes for a young person to make it in the world.”