近日，美国谷歌研究K. J. Satzinger团队研究了超导量子处理器色码的标度与逻辑。该项研究成果发表在2025年5月26日出版的《自然》杂志上。

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。最近在超导处理器上的纠错演示主要集中在表面代码上，该代码提供了很高的错误阈值，但对逻辑运算造成了限制。颜色代码能够实现更高效的逻辑，但它需要更复杂的稳定器测量和解码。在超导量子位等平面架构中测量这些稳定器是具有挑战性的，颜色代码的实现还没有解决任何平台上代码大小的性能缩放问题。 

研究组全面演示了超导处理器上的颜色代码。将代码距离从3扩展到5可以将逻辑错误抑制到∧_3/5=1.56（4）。模拟表明，这种性能低于颜色代码的阈值，在适度的设备改进后，颜色代码可能会比表面代码更有效。研究组使用逻辑随机基准测试横向Clifford门，并注入魔幻状态，这是通用计算的关键资源，通过岗位选择实现了超过99%的置信度。最后，研究组使用晶格手术在颜色代码之间传送逻辑状态。这项工作将颜色编码确立为在不久的将来在超导处理器上实现容错量子计算的一个引人注目的研究方向。

附：英文原文

Title: Scaling and logic in the color code on a superconducting quantum processor

Author: Lacroix, N., Bourassa, A., Heras, F. J. H., Zhang, L. M., Bausch, J., Senior, A. W., Edlich, T., Shutty, N., Sivak, V., Bengtsson, A., McEwen, M., Higgott, O., Kafri, D., Claes, J., Morvan, A., Chen, Z., Zalcman, A., Madhuk, S., Acharya, R., Aghababaie Beni, L., Aigeldinger, G., Alcaraz, R., Andersen, T. I., Ansmann, M., Arute, F., Arya, K., Asfaw, A., Atalaya, J., Babbush, R., Ballard, B., Bardin, J. C., Bilmes, A., Blackwell, S., Bovaird, J., Bowers, D., Brill, L., Broughton, M., Browne, D. A., Buchea, B., Buckley, B. B., Burger, T., Burkett, B., Bushnell, N., Cabrera, A., Campero, J., Chang, H.-S., Chiaro, B., Chih, L.-Y., Cleland, A. Y., Cogan, J., Collins, R., Conner, P., Courtney, W., Crook, A. L., Curtin, B., Das, S., Demura, S., De Lorenzo, L., Di Paolo, A., Donohoe, P., Drozdov, I., Dunsworth, A., Eickbusch, A., Elbag, A. Moshe, Elzouka, M., Erickson, C., Ferreira, V. S., Flores Burgos, L., Forati, E., Fowler, A. G., Foxen, B., Ganjam, S., Garcia, G., Gasca, R.

Issue&Volume: 2025-05-26

Abstract: Quantum error correction [1–4] 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 [5–8] have focused primarily on the surface code [9], which offers a high error threshold but poses limitations for logical operations. The color code [10] enables more efficient logic, but it requires more complex stabilizer measurements and decoding. Measuring these stabilizers in planar architectures like superconducting qubits is challenging, and realizations of color codes [11–19] have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor [8]. Scaling the code distance from three to five suppresses logical errors by a factor of Λ3/5 = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and the color code may become more efficient than the surface code following modest device improvements. We test transversal Clifford gates with logical randomized benchmarking [20] and inject magic states [21], a key resource for universal computation, achieving fidelities exceeding 99 % with post-selection. Finally, we teleport logical states between color codes using lattice surgery [22]. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

DOI: 10.1038/s41586-025-09061-4

Source: https://www.nature.com/articles/s41586-025-09061-4