浙江大学物理学院宋超、王浩华研究组与清华大学交叉信息研究院邓东灵研究组等合作，在超导系统中实验实现了非阿贝尔任意子的数字化量子模拟。

Topological manipulations: A graphic representing non-Abelian braiding of graph vertices in a superconducting quantum processor. (Courtesy: Google Quantum AI)

Errors are the Achilles’ heel of quantum computation, cropping up at random and threatening to ruin calculations. But they might, in principle, be tamed by encoding quantum information in a type of quasiparticle called a non-Abelian anyon. Evidence that such quasiparticles may exist has now been reported independently by teams at Google, Microsoft, the quantum-computing firm Quantinuum, and Zhejiang University in China.

The new reports “make a very intriguing advance in quantum computing”, says Jiannis Pachos, a physicist the University of Leeds, UK. “They are all things we have been waiting a long time to see,” agrees Steven Simon, a theorist at the University of Oxford, UK. “It’s a very exciting time for the field.” Still, Simon cautions that none of the results will transform quantum computing yet. “They all have shortcomings, which means there is lots of room for further work,” he says.

Quantum computers encode binary information in quantum bits, or qubits, which can take on values of 1, 0 or a superposition of the two. Various physical systems can act as qubits, including ions, photons and tiny components made from superconducting material. Quantum computations are performed by entangling many qubits so that their states are interdependent, then manipulating them according to some algorithm before reading out their final states.

The trouble is that random noise in the environment can change qubit states during the computation, making the calculation less reliable. This can happen in classical computers too, but there the problem is relatively easy to solve, for example by keeping several copies of each bit and assigning its value by majority rule. That won’t work for qubits, however, because quantum mechanics prohibits the copying of unknown quantum states, while the very nature of quantum computing requires that the qubit states remain unknown during the computation. As a result, researchers have had to search for more complicated methods of error correction.

An alternative approach is to use qubits that are more resistant to errors. In a paper written in 1997 (and published in 2003), physicist Alexei Kitaev showed that it might be possible to create error-protected qubits from hypothetical entities called Majorana particles. First proposed in 1937 by the physicist Ettore Majorana, these particles have a peculiar property: they are their own antiparticle.

No one knows whether Majorana particles exist as fundamental particles. However, Kitaev showed that they can, in principle, be created from collective states of electrons called quasiparticles. He also showed that, if used as qubits, these states would be “topologically protected”, meaning that they can’t be randomly flipped by noise without “breaking” the quasiparticle, just as you can’t get rid of the twist in a Möbius strip without cutting it. Kitaev later proposed that these Majorana quasiparticles might be engineered as electronic defect states at the ends of quantum nanowires made from (for example) a semiconductor situated close to a superconductor.

Hunting for MZMs: Azure Quantum Hardware engineer Ajuan Cui works on equipment in Microsoft’s Quantum Materials Lab (Courtesy: John Brecher/Microsoft)

To make qubits from non-Abelian anyons, Kitaev suggested moving the anyons around to weave their trajectories together. This weaving process is called braiding, and it lets the anyons swap places in a way that alters their observable states. This can then be used to perform a logic operation. Enacting a quantum algorithm thus entails braiding non-Abelian anyons in a particular way, then reading out the result.

The main benefit of this set-up is that, in effect, the topology of the braiding “remembers” the qubit states. Errors can only arise if a braid is cut, which requires a lot of energy. Under these circumstances, the computation is said to be topologically error-corrected.

In 2018, researchers in China and the UK (including Pachos) simulated the braiding of non-Abelian MZMs in an optical system. In that experiment, the quantum states corresponded to photon polarization states. The most recent results take this a step further by showing how to implement the idea in real many-qubit quantum circuits.

Hardware guy: Chetan Nayak leads the hardware programme at Microsoft’s Azure Quantum. (Courtesy: John Brecher/Microsoft)

But this has proved extremely hard, and the field has been dogged with claims that have subsequently crumbled under scrutiny. Part of the challenge has been to identify a clear signature of MZMs that distinguishes them from other quasiparticles. In their latest paper, Nayak and colleagues report evidence for what they think is a discriminating criterion for MZMs. This criterion is known as the topological gap protocol, and the Microsoft researchers say that their system – a thin film of semiconducting indium arsenide sitting below a 120-nanometre-wide strip of superconducting aluminium – passes it.

Making MZMs in such tiny objects would come with a big advantage. “In principle you could put a hell of a lot of them on a chip,” says Simon. However, the Microsoft paper is not yet peer-reviewed, and the claim will need to be checked carefully. “The hunt for MZMs has over-promised many times,” Simon adds. Though the new result looks promising, he suspects that, ultimately, claims for MZMs will only be accepted “if you can make and manipulate a qubit” from them. “Show me a qubit and then we’ll talk,” he says.

Superconducting array: The 68-qubit array used in the Zhejiang University team’s experiment. (Courtesy: Song Chao)

Cool devices: Google Quantum AI hardware engineer Catherine Erickson works on the dilution refrigerator used to cool the quantum-computing chip to the temperature necessary to distinguish the quantized energy levels of the qubits. (Courtesy: Rocco Ceselin)

The Google and Zhejiang teams used similar approaches on, respectively, a 25-qubit chip and a 68-qubit array. In both experiments, the anyons correspond to defects in a square lattice of interacting qubits, a little like dislocations in a crystal lattice. The lowest-energy (ground) state of this lattice structure consists of wavefunctions corresponding to Abelian anyons – and as Kitaev explained, this in itself can be used to construct an error-correcting qubit protected with an error-correcting code called the surface code.

To make defects corresponding to error-protected non-Abelian anyons, the researchers manipulated the interactions between neighbouring qubits in a controlled sequence. Both teams show that the resulting quasiparticles can be braided by moving them around one another. The Google researchers, led by Pedram Roushan and Trond I Andersen, also created a well-known quantum-entangled state (a Greenberger-Horne-Zeilinger or GHZ state) from their anyons – a proof of principle for how the quasiparticles can be manipulated.

The Quantinuum group, meanwhile, made non-Abelian anyons in a different way. Using the Honeywell 32-qubit H2 quantum processor, which holds ytterbium ions in an electromagnetic trap and alters their quantum states using lasers, they created a quasi-one-dimensional chain of interacting trapped-ion qubits.

Here, the anyons correspond to natural excitations of the ground state of the qubit system – which technically means they are not quasiparticles, since quasiparticles must be excited states. “The Majorana zero modes at the end of superconducting wires in the Microsoft experiment and the lattice defects in the Google experiment are non-Abelian defects,” emphasizes Ashvin Vishwanath of Harvard University, who collaborated with the Quantinuum team. “Unlike our experiment, they are not realized on top of true non-Abelian topological order.”

Trapped ions: The Quantinuum H2 processor. (Courtesy: Quantinuum)

In Roushan’s view, the two approaches to braiding non-Abelian anyons – using superconducting qubits and trapped ions – are complementary. “There are advantages and disadvantages to each approach, but it is too early to say exactly how they will impact the respective developments,” he says.

In any event, both approaches are perhaps best regarded as proofs that non-Abelian anyon states – that is, the corresponding wavefunctions – exist.  But Pachos warns that this is just a first step. “It is not clear yet how this can be moved to fault tolerance,” he says.

What is more, because these anyon states are made from conventional, error-prone qubits, no-one yet knows whether they can be made stable enough to truly act as topologically protected qubits. “To achieve fault tolerance, active error-correcting techniques will be required for our quantum simulation method,” acknowledges Song Chao, a physicist in the Zhejiang team. “A true breakthrough on the technology side will require showing that these protected qubits are more robust than the underlying qubits they are built from,” Vishwanath adds.

A further caveat is that none of the current experiments makes anyons with the right properties to provide qubits for “universal” quantum computing, which can embody any quantum algorithm. “They do have computational abilities, but none are universal,” Simon explains.

Still, all of these approaches “give a clear way to move forward”, says Pachos. He adds that “the field is very tense, as the conclusive discovery of [physical] non-Abelian anyons will lead to a Nobel prize”. But we are not there yet.

• This article was amended on 23/5/2023 to clarify Pedram Roushan’s comment on complementary approaches, and on 30/05/2023 to correct a reference to work done in 2018 by Jiannis Pachos and colleagues.

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