Fig. 2: The effect of leakage on the performance of Surface-17.
a Schematic overview of the Surface-17 layout46. Pink (resp. red) circles with D labels represent low-frequency (high-) frequency data qubits, while blue (resp. green) circles with X (Z) labels represent ancilla qubits of intermediate frequency, performing X-type (Z-type) parity checks. b Dependence of the logical error rate εL on the leakage probability L1 for a MWPM decoder (green) and for the decoding upper bound (red). The black solid line shows the physical error rate of a single transmon qubit. The dashed line corresponds to the recently achieved L1 in experiment9. Logical error rate εL for MWPM (c) and upper bound (d) as a function of the leakage conditional phases \({\phi }_{{\rm{flux}}}^{{\mathcal{L}}}\) and \({\phi }_{{\rm{stat}}}^{{\mathcal{L}}}\) (for L1 = 0.5%). Here, these phases are not randomized but fixed to the given values across all runs. The logical error rates are extracted from an exponential fit of the logical fidelity over 20 QEC cycles and averaged over 5 batches of 2 × 104 runs for b and one batch of 2 × 104 runs for c, d Error bars correspond to 2 standard deviations estimated by bootstrapping (not included in b due the error bars being smaller than the symbol size).
