The resources are counted as the number of two-qubit CNOT gates for non-EASE-based implementation and multi-qubit EASE gates for EASE-based implementation. The quantum computational runtime or fidelity of the algorithms may vary in practice. See Fig. 3 for the details of the trade-off between the two approaches for the particular context described therein. Well-defined circuit layouts of the two-qubit entangling gates in all cases considered allow for negligible classical resource overhead in solving for EASE pulse shapes over the standard pairwise pulse shapes used in a serial approach. Shown are the Hamiltonian simulation (HSIM) algorithms (circles) simulating the Heisenberg Hamiltonian over various connectivity structures10, variational quantum eigensolver (VQE) circuits (triangles) simulating the water molecule with varying degrees of approximations23, quantum Fourier transform (QFT) circuits (red lines)21, and Bernstein–Vazirani (BV) algorithm (orange lines)22 with expected gate counts over all possible oracles of a fixed size. Hollow plot symbols and dashed lines denote the two-qubit CNOT gate based implementations. Solid plot symbols and solid lines denote the multi-qubit EASE-based implementations. Quadratic improvements in the resource requirement are observed for HSIM and QFT, and a linear to constant complexity improvement is observed for the BV and the Hidden-shift (not shown) algorithms. See Supplementary Note 4 for details on how to obtain EASE-gate counts.