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Realizing the potential of quantum computing requires sufficiently low logical error rates. Many applications call for error rates as low as 10⁻¹⁵ (refs. ^{, , , , , , –}), but state-of-the-art quantum platforms typically have physical error rates near 10⁻³ (refs. ^{, , , –}). Quantum error correction^{, –} 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. 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. 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 …