Fig. 5: Performance of a greedy Pauli grouping algorithm with various solvers from Table 3.

a–c Estimated shot reduction \({\hat{R}}_{{\rm{HT}}}/{\hat{R}}_{{\rm{TPB}}}\) for three classes of n-qubit Hamiltonians O. The HT readout circuits assume a linear hardware connectivity. Different curves correspond to different solvers from Table 3 and, in the case of random Hamiltonians (b, e, h), to different numbers M of Pauli operators in O. For the single data point with the red star symbol (⋆) at n = 14 in (c and f), we use the restr. alg. solver with a fine-tuned choice of hyperparameters. d–f Runtime of our HT Pauli grouping algorithm. g–i Estimated shot reduction \({\hat{R}}_{{\rm{GC}}}/{\hat{R}}_{{\rm{TPB}}}\) that is in principle achievable with unrestricted Clifford circuits if two-qubit errors are neglected, which is an unrealistic assumption for near-term quantum devices. Therefore, HT readout circuits present the best viable option in this comparison. See “Methods” for further details.