Fig. 2: Error detection in the surface code.

a, Illustration of a surface code experiment, in perspective view with time progressing to the right. We begin with an initial data qubit state that has known parities in one stabilizer basis (here, Z). We show example errors that manifest in detection pairs: a Z error (red) on a data qubit (spacelike pair), a measurement error (purple) on a measure qubit (timelike pair), an X error (blue) during the CZ gates (spacetimelike pair) and a measurement error (green) on a data qubit (detected in the final inferred Z parities). b, Detection probability for each stabilizer over a 25-cycle distance-5 experiment (50,000 repetitions). Darker lines: average over all stabilizers with the same weight. There are fewer detections at timestep t = 0 because there is no preceding syndrome extraction, and at t = 25 because the final parities are calculated from data qubit measurements directly. QEC, quantum error correction. c, Detection probability heatmap, averaging over t = 1 to 24. d,e, Similar to b,c for four separate distance-3 experiments covering the four quadrants of the distance-5 code. f,g, Similar to b,c using a simulation with Pauli errors plus leakage, crosstalk and stray interactions (Pauli+). h, Bar chart summarizing the detection correlation matrix p_ij, comparing the distance-5 experiment from b to the simulation in f (Pauli+) and a simpler simulation with only Pauli errors. We aggregate four groups of correlations: timelike pairs; spacelike pairs; spacetimelike pairs expected for Pauli noise; and spacetimelike pairs unexpected for Pauli noise (Unexp.), including correlations over two timesteps. Each bar shows a mean and standard deviation of correlations from a 25-cycle, 50,000-repetition dataset.