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

Abstract

Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical 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. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes 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, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of ${\Lambda }_{3/5}$ = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

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Cited by in corpus (18)

• Demonstration of low-overhead quantum error correction codes
• Realizing Lattice Surgery on Two Distance-Three Repetition Codes with Superconducting Qubits
• Quantum error correction for long chains of trapped ions
• Demonstration of two-dimensional connectivity for a scalable error-corrected ion-trap quantum processor architecture
• Quantum error detection in qubit-resonator star architecture
• Fundamental thresholds for computational and erasure errors via the coherent information
• Lattice surgery-based logical state teleportation via noisy links
• Decoding across transversal Clifford gates in the surface code
• Lattice Surgery Compilation Beyond the Surface Code
• Efficient simulation of logical magic state preparation protocols
• Fault-tolerant interfaces for modular quantum computing on diverse qubit platforms
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• Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction