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Single-shot error correction corrects data noise using only a single round ofnoisy measurements on the data qubits, removing the need for intensivemeasurement repetition. We introduce a general concept of confinement forquantum codes, which roughly stipulates qubit errors cannot grow withouttriggering more measurement syndromes. We prove confinement is sufficient forsingle-shot decoding of adversarial errors and linear confinement is sufficientfor single-shot decoding of local stochastic errors. Further to this, we provethat all three-dimensional homological product codes exhibit confinement intheir $X$-components and are therefore single-shot for adversarial phase-flipnoise. For local stochastic phase-flip noise, we numerically explore thesecodes and again find evidence of single-shot protection. Our Monte Carlosimulations indicate sustainable thresholds of $3.08(4)\%$ and $2.90(2)\%$ for3D surface and toric codes respectively, the highest observed single-shotthresholds to date. To demonstrate single-shot error correction beyond theclass of topological codes, we also run simulations on a randomly constructed3D homological product code.

Single-shot error correction of three-dimensional homological product codes