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Google Research, Mountain View, CA, USA.
Department of Physics, ETH Zurich, Zurich, Switzerland.
Nature. 2025 May 26. doi: 10.1038/s41586-025-09061-4.
Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. The colour code enables more efficient logic, but it requires more complex stabilizer measurements and decoding. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and realizations of colour codes have not addressed performance scaling with code size on any platform. Here we present a comprehensive demonstration of the colour code on a superconducting processor. Scaling the code distance from three to five suppresses logical errors by a factor of Λ = 1.56(4). Simulations indicate this performance is below the threshold of the colour code, and the colour code may become more efficient than the surface code following modest device improvements. We test transversal Clifford gates with logical randomized benchmarking and inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection. Finally, we teleport logical states between colour codes using lattice surgery. This work establishes the colour code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.
量子纠错对于弥合物理设备的错误率与量子算法所需的极低错误率之间的差距至关重要。近期在超导处理器上进行的纠错演示主要集中在表面码上，表面码具有较高的错误阈值，但在逻辑操作方面存在局限性。颜色码能实现更高效的逻辑，但需要更复杂的稳定器测量和解码。在诸如超导量子比特等平面架构中测量这些稳定器具有挑战性，并且在任何平台上，颜色码的实现都尚未解决随着码大小的性能扩展问题。在此，我们展示了在超导处理器上对颜色码的全面演示。将码距从三扩展到五可将逻辑错误抑制1.56(4)倍。模拟表明这种性能低于颜色码的阈值，并且在对器件进行适度改进后，颜色码可能会比表面码更高效。我们使用逻辑随机基准测试来测试横向克利福德门，并注入魔法态（通用计算的关键资源），通过后选择实现了超过99%的保真度。最后，我们使用晶格手术在颜色码之间隐形传态逻辑态。这项工作确立了颜色码作为在不久的将来实现超导处理器上容错量子计算的一个有吸引力的研究方向。
