The work is a step toward crash-proof quantum computers:
In 1997, Alexei Kitaev, a theorist at the California Institute of Technology, pointed out that such quasiparticles could lay the perfect foundation for quantum computers. Physicists have long salivated at the possibility of harnessing the quantum world to perform calculations beyond the reach of typical computers and their binary bits. But qubits, the atomlike building blocks of quantum computers, are fragile. Their wave functions collapse at the lightest touch, erasing their memories and their ability to perform quantum calculations. This flimsiness has complicated ambitions to control qubits long enough for them to finish lengthy calculations.
Kitaev realized that the shared memory of non-abelian anyons could serve as an ideal qubit. For starters, it was malleable. You could change the state of the qubit — flipping a zero to a one — by exchanging the positions of the anyons in a manner known as "braiding."
You could also read out the state of the qubit. When the simplest non-abelian anyons are brought together and "fused," for instance, they will emit another quasiparticle only if they have been braided. This quasiparticle serves as a physical record of their crisscrossed journey through space and time.
And crucially, the memory is also nigh incorruptible. As long as the anyons are kept far apart, poking at any individual particle won't change the state the pair is in — whether zero or one. In this way, their collective memory is effectively cut off from the cacophony of the universe.
"This would be the perfect place to hide information," said Maissam Barkeshli, a condensed matter theorist at the University of Maryland.
Kitaev's proposal came to be known as "topological" quantum computing because it relied on the topology of the braids. The term refers to broad features of the braid — for example, the number of turns — that aren't affected by any specific deformation of their path. Most researchers now believe that braids are the future of quantum computing, in one form or another. Microsoft, for instance, has researchers trying to persuade electrons to form non-abelian anyons directly. Already, the company has invested millions of dollars into building tiny wires that — at sufficiently frigid temperatures — should host the simplest species of braidable quasiparticles at their tips. The expectation is that at these low temperatures, electrons will naturally gather to form anyons, which in turn can be braided into reliable qubits.
After a decade of effort, though, those researchers are still struggling to prove that their approach will work. A splashy 2018 claim that they had finally detected the simplest type of non-abelian quasiparticle, known as "Majorana zero modes," was followed by a similarly high-profile retraction in 2021. The company reported new progress in a 2022 preprint, but few independent researchers expect to see successful braiding soon.
Similar efforts to turn electrons into non-abelian anyons have also stalled. Bob Willett of Nokia Bell Labs has probably come the closest in his attempts to corral electrons in gallium arsenide, where promising but subtle signs of braiding exist. The data is messy, however, and the ultracold temperature, ultrapure materials, and ultrastrong magnetic fields make the experiment tough to reproduce.
"There has been a long history of not observing anything," said Eun-Ah Kim of Cornell University.
Wrangling electrons, however, is not the only way to make non-abelian quasiparticles.
"I had given up on all of this," said Kim, who spent years coming up with ways to detect anyons as a graduate student and now collaborates with Google. "Then came the quantum simulators."
[...] Last fall, Kim and Yuri Lensky, a theorist at Cornell, along with Google researchers, posted a recipe for easily making and braiding pairs of defects in the toric code. In a preprint posted shortly after, experimentalists at Google reported implementing that idea, which involved severing connections between neighboring qubits. The resulting flaws in the qubit grid acted just like the simplest species of non-abelian quasiparticle, Microsoft's Majorana zero modes.
"My initial reaction was 'Wow, Google just simulated what Microsoft is trying to build. It was a real flexing moment," said Tyler Ellison, a physicist at Yale University.
By tweaking which connections they cut, the researchers could move the deformations. They made two pairs of non-abelian defects, and by sliding them around a five-by-five-qubit chessboard, they just barely eked out a braid. The researchers declined to comment on their experiment, which is being prepared for publication, but other experts praised the achievement.
[...] The technique had a dark side that initially doomed researchers' attempts to make non-abelian phases: Measurement produces random outcomes. When the theorists targeted a particular phase, measurements left non-abelian anyons speckled randomly about, as if the researchers were trying to paint the Mona Lisa by splattering paint onto a canvas. "It seemed like a complete headache," Verresen said.
Toward the end of 2021, Vishwanath's group hit on a solution: sculpting the wave function of a qubit grid with multiple rounds of measurement. With the first round, they turned a boring phase of matter into a simple abelian phase. Then they fed that phase forward into a second round of measurements, further chiseling it into a more complicated phase. By playing this game of topological cat's cradle, they realized they could address randomness while moving step by step, climbing a ladder of increasingly complicated phases to reach a phase with non-abelian order.
"Instead of randomly trying measurements and seeing what you get, you want to hop across the landscape of phases of matter," Verresen said. It's a topological landscape that theorists have only recently begun to understand.
