Fig. 2: Optimization and healing performance.

a CZXEB cycle error benchmarks (e_c, boxes, left axis) and calibration failures (gray bars, right axis in (c)) for the random baseline (red), outlier (orange diamond), and crossover (green) performance standards used to evaluate frequency configurations and our optimization strategy. Each box shows the 2.5, 25, 50, 75, and 97.5th percentiles and mean (see annotations on the baseline). The standards' means are extended across panels for comparison. b Benchmarks for configurations optimized at different scopes (S) ranging from S = 1 (local limit, 1D optimization) to \(S={S}_{\max }\) (global limit, ∣F∣D optimization). Intermediate dimensional optimization (2 ≤ S ≤ 4) outperforms both local and global optimization, finding configurations near the crossover standard. S = 4 (≤21D optimization) performs best, with the lowest mean error, but S = 2 (≤5D optimization) offers a better balance between performance and runtime, and is set as our default. c Benchmarks for each configuration in (b) after healing, which significantly suppresses performance outliers. Each box in (a), (b), and (c) corresponds to a distinct configuration. d Benchmark heatmaps illustrating optimization and (e) healing of targeted gates in the S = 5 (≤29D optimization) configuration. Each hexagon corresponds to the cycle error for one pair (e_c,ij). Performant gates are blue, outliers are red, and unoptimized and targeted gates are gray.