These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device 18, 19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Crucially, this error suppression is stable over 50 rounds of error correction. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Quantum error correction 15, 16, 17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. 2, 3, 4, 5, 6, 7, 8, 9), but state-of-the-art quantum platforms typically have physical error rates near 10 −3 (refs. Many applications call for error rates as low as 10 −15 (refs. Realizing the potential of quantum computing requires sufficiently low logical error rates 1.
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