Forty years ago, Frank Wilczek was thinking about a strange particle that could only survive in a two-dimensional universe. After calculations, Wilchek found that these theoretical particles have extraordinary memories that are so deeply integrated into macroscopic reality that no interference can erase them.
Researchers have spent millions of dollars over the past three decades or so trying to capture the particles, known as non-abelian anyons. Now, two landmark papers have finally achieved this goal.
First, physicists recently announced that they have synthesized and manipulated non-abelian anyons using state-of-the-art processors.
Second, the experiment is based on a proof of concept presented by Google researchers last fall, that information can be stored and manipulated in memories shared by non-abelian assorts.
The two papers demonstrate the growing capabilities of quantum devices while providing a peek into the future of quantum computing: by keeping a virtually indestructible record of traveling through space and time, non-abelian anyons may be the best solution for building quantum computers.
Flatland Computing
In 1982, Wilczek helped physicists expand their minds to understand the kinds of particles that could exist in two-dimensional space. He studied limiting quantum laws to a completely flat hypothetical universe and found that this universe would contain strange particles with fractional spins and charges. Although these particles may not be distinguishable in some ways, in a two-dimensional physics system, swapping their position may change their state, which is not possible in a three-dimensional physics system. Wilchek named these two-dimensional particles anyons because they seemed to do almost anything.
Wilchek focused on the simplest abelian anyons, particles that change in subtle ways that cannot be detected when exchanged.
He didn't explore the more exotic example of non-abelian ascensions, particles that share memories. Swapping the positions of two non-abelian anyons produces a directly observable effect. This changes the state of the wave function they share, which is a quantity that describes the quantum properties of a system. If you encounter two identical non-abelian anysons, by measuring which state they are in, you can tell if they have been in those positions all the time, or if their paths have crossed — something that no other particle can do.
The concept seems too exotic to develop into a formal theory.
But in 1991, two physicists found these states. They predicted that when subjected to a strong enough magnetic field and a low enough temperature, the electrons would rotate in the right way, forming non-abelian asions. These anyons are not elementary particles (forbidden in the 3D world), they are "quasiparticles". Quasiparticles are collections of particles, but it's best to think of them as separate units. Quasiparticles have precise positions and behaviors, just as a collection of water molecules creates waves and swirls.
In 1997, theorist Alexei Kitaev of the California Institute of Technology showed that such quasiparticles could provide the perfect foundation for quantum computers. But the building blocks of quantum computers, qubits, are fragile. Their wave function collapses at the slightest perturbation, erasing their memory and ability to perform quantum calculations. This fragility makes quantum computing difficult to achieve.
Kitayev realized that the shared memory of non-abelian assortments could serve as ideal qubits. First, it's malleable. The state of a qubit can be changed by swapping the position of any electron in a way called "braiding" — flipping zero to 1.
You can also read out the state of the qubit. For example, when the simplest non-abelian anyons are clustered together and "fused," they emit another quasiparticle only if they are woven together. This quasiparticle serves as a physical record of their intersection in space and time.
Most importantly, memory can hardly be destroyed. As long as any of the particles are kept far enough apart, touching any individual particle will not change the state of the pair of particles—whether 0 or 1. In this way, their collective memory is effectively isolated from the noise of the universe. This is the perfect place to hide information.
Hard-to-navigate electronics
Kitaev's proposal is called "topological" quantum computing because it relies on woven topologies. The term refers to the broad features of the weave – for example, the number of rotations – that are not affected by any particular deformation of their path. Most researchers now believe that weaving is the future of quantum computing. For example, Microsoft has researchers trying to get electrons to form non-abelian asons directly. Microsoft has invested millions of dollars to make tiny wires that, at low enough temperatures, should be able to generate the simplest kinds of quasiparticles that can be woven on top of them.
The expectation is that, at these low temperatures, electrons naturally aggregate into arbitrary particles, which can then be woven into reliable qubits. However, after a decade of work, these researchers are still trying to prove that their method works. Efforts to convert electrons into non-abelian arbitrons have stalled.
However, harnessing electrons is not the only way to make non-abelian quasiparticles.
Compatible qubits
Quantum processors are changing the way arbitrary particles are found. In recent years, researchers have begun using these devices to control individual qubits, rather than trying to get large numbers of electrons to act in unison. Some physicists think of these efforts as simulations because the qubits inside the processor are abstractions of particles (although their physical properties vary from lab to lab, you can think of them as particles rotating around an axis). But the quantum nature of qubits is real, so — analog or not — these processors have become the best space for topological experiments.
Synthesizing anyons on quantum processors is another way to take advantage of Kitaev's weaving theory: accept that qubits are imperfect, and correct their mistakes. Inferior qubits don't live long, so any tons built by them will also have a short lifespan. The dream is to measure qubit groups quickly and repeatedly, and correct errors as soon as they occur, thereby extending the lifetime of anyons. The measurement erases the quantum information of a single qubit by collapsing its wave function and turning it into a classical bit. But important information remains untouchable—hidden in the collective state of many arbitrary children. In this way, Google and other companies hope to reinforce qubits by measuring quickly and correcting them quickly instead of cryogenic temperatures.
Google took a major step toward quantum error correction in the spring of 2021, when researchers assembled about 24 qubits into the simplest mesh capable of quantum error correction, a phase of matter known as toric code.
Creating torus coding on Google's processor is equivalent to making each qubit strictly cooperate with its neighboring qubits by gently pushing them with microwave pulses. Without making a measurement, qubits point to a superposition state in multiple possible directions. Google's processor effectively reduces these options (the various directions a qubit might point to) by making each qubit coordinate its spin axis with its four neighboring qubits in a specific way. Although torus coding has topological properties that can be used for quantum error correction, it does not contain non-abelian quasiparticles itself. To do so, Google had to resort to a strange trick that theorists have long known: certain flaws in qubit grids called "distortion defects" can obtain non-abelian quasiparticles.
Last fall, Cornell theorists Yuri Lensky and researchers at Google published a scheme for easily making and weaving defect pairs in torus coding.
In a preprint released after that, Google's experimenters reported ideas for implementing the solution, including cutting the connection between adjacent qubits. Flaws in qubit grids are like the simplest non-abelian quasiparticles, Microsoft's Majorana Zero Mode.
Weaving quantum information: By carefully manipulating the connections between qubits, researchers were able to weave objects together with memories of their past.
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By adjusting the connections they cut, the researchers could control the deformation. They made two pairs of non-abelian defects and slid them over a grid of five-by-five qubits, barely weaving a braid.
Painting by measurement
Meanwhile, a group of theorists led by Ashvin Vishwanath of Harvard University is pursuing a higher goal: creating true non-abelian anyons in a more complex quantum phase of matter, quasiparticles that occur naturally in the primordial phase of matter. By contrast, Google's "flaw" is like a baby-level non-abelian thing.
Both types of anyons are in phases of matter with topological properties defined by intricate quantum entanglements. Particles in an entangled state exhibit coordinated behavior, and when trillions of particles are entangled, they can fluctuate in complex phases. In phases with a topological order, entanglement organizes particles into aligned spin rings. When a ring is cut, each endpoint is an arbitrary sub.
There are two types of topological order. Simple phases like torus coding have an " abelian order " with loose ends in abelian anyons. But researchers seeking true non-abelian arbitrarins set their sights on a completely different, more complex fabric with a non-abbe order.
In 2021, Vishwanath's group helped create a phase with an abelian order. But weaving qubits into non-abelian entanglement patterns is too complicated for today's unstable processors. So the team pored over the literature to look for new ideas.
They found a clue in two papers:
In general, we need to handle qubits carefully, which is like tidying up a pillow, you have to be careful so that the filling of the pillow does not fly out of the gap. In other words, you need to operate in a gentle way to maintain the integrity of the quantum state. At the same time, carefully weaving the entanglement between qubits through these "unitary" operations, that is, operations that keep the overall properties of the system unchanged, takes time.
However, in the early 2000s, physicist Robert Rauschdorff found a shortcut to use measurements to remove parts of the wave function. In quantum mechanics, measurements often lead to the collapse of quantum states, eliminating the properties of quantum. But Rauschdorf found that he could use this property as a tool to adjust quantum states faster through purposeful measurements, which in turn would speed up the computational process to some extent.
Rauschdorf and his collaborators describe in detail how a non-entangled state can be intentionally transformed into an entangled state by selective measurements of specific qubits.
This technique has a drawback, initially preventing researchers from making non-abelian phases: measurements produce random results. When theorists aim for a particular phase, the measurements cause non-abelian isons to randomly scatter everywhere, as if a researcher were trying to paint the Mona Lisa by splashing paint on a canvas.
At the end of 2021, Vishwanath's group found a solution: sculpting the wave function of a qubit grid through multiple rounds of measurements. Through the first round of operations, they transformed an ordinary material phase into a simple abelian phase. They then fed the results of this stage into a second round of measurements, further shaping a more complex phase of matter. By playing this game of topology, they realized that they could handle randomness while progressing step by step. By climbing the increasingly complex phase ladder step by step, we finally reach the stage of non-abelian order.
Last summer, the team tested their theory on Quantinuum's H1 ion processor, one of the few quantum devices that can make measurements instantaneously. Like Google's group, they made Abel's ring code and weaved its non-Abel flaws. They tried to reach non-abelian phases, but only 20 qubits could not reach them.
Their experiments marked the first indisputable detection of non-abelian phases. Implementing a non-abelian topological order is something that people have wanted to do for a long time, and this is an important milestone.
Their work culminated in the weaving of three pairs of non-abelian anysons, allowing their trajectories in space and time to form a pattern known as Borromean rings, the first time non-abelian anyons were weaved. Three Borromean rings are inseparable when they are together, but if you cut one, the other two will separate.
foreground
Creating topological phases on a quantum processor is like making the world's smallest chunks of ice by stacking dozens of water molecules. The most exciting aspect of these experiments is their implications for quantum computing: researchers have finally shown that they can make the necessary ingredients. Now they just need to figure out how to actually put them to work. One problem is that there are a large number of different kinds of arbitraris, each with its own advantages and disadvantages. For example, some people have richer memories of their past, making their weaving more numerous.
The next milestone will be a real error correction, something neither Google nor Quantinuum has tried. The qubits they weave are hidden but unprotected, which will require measuring inferior subbits underneath and quickly fixing their bugs in real time. Such a demonstration would be a watershed moment for quantum computing, but it could be years away.
Until then, optimists hope these recent experiments will start a cycle in which more advanced quantum computers can better control non-abelian quasiparticles, which in turn will help physicists develop more capable quantum devices.
Source: Quantamagazine