Hardware-efficient error correction: cat states make quantum chips more robust

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Although the first prototypes of quantum computers already exist, they are still very prone to errors. In order to be able to solve relevant problems with them in the future, research groups are trying to correct calculation errors in the qubits during runtime. A team led by Harald Putterman from the Amazon Web Services (AWS) Center for Quantum Computing in Pasadena, California, has now shown that this may be possible with far fewer qubits than previously thought.

In their experiment, the researchers used so-called cat qubits from superconducting circuits, which are resistant to a certain type of noise. They therefore only had to correct a second type of error. Their approach required far fewer qubits than other concepts. They showed this in a paper published today, Wednesday, im journal Nature.

Correcting errors in quantum computers

The reason for the high susceptibility to errors of today's quantum computers is the unstable nature of their basic building blocks, the qubits. Although developers try to make their qubits as stable as possible, the information stored in them is inevitably lost over time. In addition, errors occur during the execution of computing operations, so that results become noisy and unusable.

The aim of quantum error correction is to prevent this. The basic idea is to combine a large number of qubits and distribute the information across all qubits. Additional calculation steps then make it possible to detect and correct errors without affecting the actual calculation. Together, these physical qubits form an error-corrected logical qubit.

Experts previously estimated that thousands of physical qubits could be needed to generate an error-corrected logical qubit. Since hundreds or thousands of these could be needed to solve relevant problems with a quantum computer, this approach places extreme demands on the hardware.

"The development of quantum computers is currently very much about error correction," says Hannes Bernien, Professor of Physics at the University of Innsbruck and Scientific Director at the Institute for Quantum Optics and Quantum Information in Vienna. For example, a Forschungsteam around Julian Kelly from Google Quantum AI demonstrated the effective correction of quantum errors for the first time at the end of 2024. The team constructed a logical qubit from 17, 49 and 97 physical qubits and showed that the error of the logical qubit decreased exponentially when more qubits worked together. With even larger numbers of qubits, the error rate could be reduced even further.

Cat states in a ladder

Harald Putterman from AWS and his US-Israeli team are pursuing a different approach. They use so-called cat states, or "cat qubits", to encode the information. These are named after the famous thought experiment about Schrödinger's cat.

"Conventional qubits are two-state systems. For example, they can exist in two different energy states," explains Bernien. These two states are normally referred to as 0 and 1. "The cat qubits used here are bosonic qubits. Here, the energy states are those of a harmonic oscillator." This has not just two states, but an infinite number of them, similar to an infinitely long ladder.

In order to bring it into a cat state, the researchers superimpose two states that are as opposite as possible – similar to Schrödinger's cat, which is dead and alive at the same time. These two possibilities then correspond to the binary states 0 and 1, their superposition is the cat state.

Robust against errors

The advantage of these special cat qubits is that they are very robust against a certain type of error, known as bit flip errors. Here, a qubit randomly flips back and forth between the two switch positions 0 and 1 over time, for example due to decay processes. "By cleverly encoding a qubit in their large state space, Cat qubits are very robust against bit flip errors," says Bernien. Therefore, no additional correction of these errors is necessary.

"The approach of cat qubits is not new and it has already been shown in recent years that they are quite stable. The interesting thing about the new publication is that several cat qubits have been combined," says the researcher. The reason for this is that cat qubits are very susceptible to another type of error, known as phase errors. These are particularly relevant when qubits are in superposition states, as is the case with cat qubits.

By combining several cat qubits with each other, the researchers can execute a so-called repetition code and correct phase errors, as Michael Hartmann, Professor of Theoretical Physics at Friedrich-Alexander-Universität Erlangen-Nürnberg, explains. "For example, instead of a 1, a 111 is stored in three qubits. If a bit flip error occurs on a qubit – that turns its 1 into a 0 –, you can see from the other two ones that an error must have occurred that can be corrected." In contrast to the surface code used by Google researchers, for example, this form of error correction has a simpler structure and can be implemented with a linear chain of building blocks.

In this way, the researchers need far fewer qubits to correct errors. "With superconducting qubits, it is expected that several thousand qubits will be needed to store the information with sufficient redundancy so that all errors can be corrected," says Hartmann. "A sophisticated quantum computer with cat qubits can manage with considerably fewer qubits – depending on the quality of the implementation with a tenth or hundredth of the qubits."

Five cat qubits correct errors

Specifically, the researchers combined up to five cat qubits from superconducting circuits, similar to the qubits used by Google and IBM, for example. These consist of microwave resonators containing photons. These photons are superimposed and together form a cat qubit. The more photons are superimposed per cat qubit, the more bit flip errors are suppressed. At the same time, however, the number of phase errors increases. "In the best-case scenario, this approach can be used to find a 'sweet spot' in the future in which the bit-flip errors can be suppressed long enough for calculations and phase errors can be corrected," says Bernien.

In their publication, the AWS researchers show that they were able to reduce the error rate to 1.65 percent per computing cycle using five cat qubits, compared to 1.75 percent with three cat qubits. The error rate is therefore below the relevant threshold for error correction, says Stefan Filipp, Professor of Technical Physics at the Technical University of Munich (TUM). "However, with an error rate of just over 1.5 percent for a logical qubit, this is still high and future improvements must significantly reduce this error rate before practical algorithms can actually be performed."

Further research needed

In addition, much larger systems are still needed, says Filipp. According to the authors, the method has the potential to scale efficiently. However, they point out that they need to further optimize their approach to improve performance and show practical relevance. The advantage, according to Filipp, is that the researchers can directly exploit the scaling potential of superconducting qubit platforms, as several hundred qubits have already been realized. In principle, this architecture is also well suited for mass production using micro- and nanofabrication processes.

The researchers are also not yet using the cat qubits for computing operations, notes Hartmann. "No algorithms have yet been performed on cat qubits," in contrast to other architectures. "The continued success of cat qubits will depend heavily on how well the scaling really works and how well the property that an error type almost never occurs can be maintained in all gating and readout operations. These things are not yet sufficiently realized."

However, Bernien sees the great advantage of cat qubits in the fact that fewer physical cat qubits are required for an error-corrected, logical qubit than conventional qubits. "This is a worthwhile approach when you consider that it is not trivial to produce and combine qubits," he says. He does not yet see a breakthrough in the work. However, the researchers have at least demonstrated that their approach to error correction works in principle experimentally. "They show that it may be worth looking at other types of qubits as well."

(spa)