Scaling and logic in the colour code on a superconducting quantum processor.

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 code⁹, which offers a high error threshold but poses limitations for logical operations. The colour code¹⁰ 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^11-19 have not addressed performance scaling with code size on any platform. Here we present a comprehensive demonstration of the colour code on a superconducting processor⁸. Scaling the code distance from three to five suppresses logical errors by a factor of Λ_3/5 = 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 benchmarking²⁰ and inject magic states²¹, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection. Finally, we teleport logical states between colour codes using lattice surgery²². This work establishes the colour code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.