Short answer: Color codes and surface codes are two families of topological quantum error-correcting codes, and three arXiv papers from 2014, 2016 and 2025 compare them in theory. They find trade-offs in qubit counts, gate speed and decoding thresholds that depend on the noise model. All three are preprints of simulation and analysis, and none reports a hardware experiment.
What is the comparison about?
The 2025 arXiv preprint says color codes have advantages for fault-tolerant quantum computing, such as high encoding rates and transversal implementation of Clifford gates. The 2014 preprint on lattice surgery describes planar topological codes as promising for fault-tolerant computing because of their high thresholds, compatibility with two-dimensional local processing and other properties. The question these papers address is when each family needs fewer resources or tolerates more noise.
What did the 2014 lattice-surgery paper find?
The authors show how to use lattice surgery to perform a universal set of fault-tolerant operations with color codes, and they improve existing surface-code lattice-surgery methods along the way. They state that lattice-surgery methods use fewer qubits and the same time or less than defect-braiding methods, and that per code distance, color-code lattice surgery uses approximately half the qubits and the same time or less than surface-code lattice surgery. Color-code lattice surgery can also implement Hadamard and phase gates in a single transversal step, which they say is much faster than in surface-code lattice surgery. Against uncorrelated circuit-level depolarizing noise, they report that color-code lattice surgery uses fewer qubits for the same error suppression when the noise rate is low enough and the demand for suppression is high enough.
What did the 2016 paper compare?
The 2016 preprint considers the smallest examples of several topological code families, surface codes, color codes and the gauge color code, and asks what is the minimum needed to demonstrate error suppression. The authors say it is likely that first demonstrations of suppression of quantum noise with small topological codes will soon be possible, so clear, achievable performance metrics are needed. They use an exact decoder, simple models of physical error and measurement error, and determine regions of correctability in the physical parameters for each code.
What does the 2025 decoder paper report?
The authors note that existing matching-based decoders for color codes, such as the restricted decoder, have limited performance. They introduce a correlated decoder for the 4.8.8 color code, built by mapping the correlated matching decoder for the surface code onto the color code lattice. Analytical and numerical results show higher thresholds than the restricted and unified decoders, and equal performance to the unified decoder at very low physical error rates. They estimate color-code thresholds against bit-flip error of 10.38 percent under the code capacity model and 3.13 percent under the phenomenological model, and thresholds of 16.62 percent and 3.52 percent for the surface code against depolarizing noise through the surface-color mapping.
What to keep in mind
Thresholds depend strongly on the noise model, so the 2025 figures for code capacity and phenomenological noise are not comparable with circuit-level results such as those in the 2014 work. All three papers are arXiv preprints, so these statements are the authors' claims. This post relies on abstracts and visible summary text and full texts were not checked. It makes no claim about products or built systems.
FAQ
What is a transversal gate?
A gate applied independently to each physical qubit. The 2025 abstract lists transversal Clifford gates as an advantage of color codes.
Do color codes use fewer qubits than surface codes?
In the 2014 lattice-surgery analysis, per code distance they use about half, under the conditions stated there.
What threshold was reported in 2025?
10.38 percent for color codes against bit-flip error under code capacity noise, and 3.13 percent under phenomenological noise.
Has any of this been demonstrated on hardware?
Not in these abstracts, which cover theory and numerical simulation.
All field notes