A color code experiment on a superconducting processor

Short answer: A 2025 Nature paper, with a preprint version posted in December 2024, reports a demonstration of the color code on a superconducting processor, with logical error suppression as the code distance grows from three to five. The authors say transversal Clifford gates added little error compared with an idling correction cycle. These are the authors' reported results on their own device, and the abstract was only partly readable.

Why the color code

The abstract says quantum error correction is essential for bridging the gap between physical error rates and the very low logical error rates needed for quantum algorithms. It notes that recent demonstrations on superconducting processors have focused mainly on the surface code, which has a high threshold but limits on logical operations. The color code, the authors say, enables much more efficient logic, although it needs more complex stabilizer measurements and decoding. Measuring these stabilizers in planar architectures such as superconducting qubits is described as challenging. They add that earlier color code realizations had not addressed performance scaling with code size on any platform.

What the paper reports

The authors present what they call a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor they give as 1.56 with an uncertainty of 0.04. They say simulations indicate this performance is below the threshold of the color code, and that the color code may be more efficient than the surface code with modest device improvements. That last point is a simulation-based projection, not a measurement.

Using logical randomized benchmarking, they report that transversal Clifford gates add an error of only 0.0027, with an uncertainty of 0.0003, which they say is substantially less than the error of an idling error correction cycle.

What is not covered here

The abstract continues past that point, but the remainder could not be read in full when this post was written, so nothing further from it is described.

How to read the numbers

The suppression factor compares logical error at distance five with distance three, so it speaks to scaling with code size, which the abstract says earlier color code realizations had not addressed. A factor above one means the larger code did better, which is the direction error correction needs. The gate result is a different kind of figure: it describes the extra error from transversal Clifford gates, measured with logical randomized benchmarking, set against the error of an idling cycle. The two figures answer separate questions and are not combined into one score in the abstract.

Limits

A factor of 1.56 is modest suppression at small distances, and it comes from one experiment on one processor. The efficiency comparison with the surface code relies on simulation and on device improvements that have not been shown. The published Nature version and the preprint are the same work, so they should not be counted as independent confirmation.

FAQ

What did the experiment demonstrate?

A color code on a superconducting processor with logical error suppression and logical operations, per the authors.

How much did errors drop from distance three to five?

By a factor of 1.56, with an uncertainty of 0.04, as reported by the authors.

Is the color code better than the surface code?

The authors say simulations suggest it may be more efficient with modest device improvements. That is not a measured result.

How well did transversal Clifford gates perform?

They add an error of 0.0027, with an uncertainty of 0.0003, which the authors say is less than an idling cycle.

Does this mean fault tolerant computing is here?

No. It is a small-distance experiment.