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The surface code is a promising candidate for fault-tolerant quantumcomputation, achieving a high threshold error rate with nearest-neighbor gatesin two spatial dimensions. Here, through a series of numerical simulations, weinvestigate how the precise value of the threshold depends on the noise model,measurement circuits, and decoding algorithm. We observe thresholds between0.502(1)% and 1.140(1)% per gate, values which are generally lower thanprevious estimates.

Fault-tolerant thresholds for quantum error correction with the surface code