Fig. 2. Flowchart for EASE-gate pulse-shape synthesis.

As a preprocessing step, reorder those qubits that participate in a given EASE gate into disjoint, non-interacting sets, where the first and second qubits of each set interact. In other words, within each set, overlapping qubit pairs may interact, if the size of the set is larger than two. Consider now the following iterative steps. In Step 1, identify the qubits considered in the past iterations that do not interact with the currently considered qubit. In Step 2, construct a subspace orthogonal to the interactions between previously determined pulse shapes for qubits identified in Step 1 and the currently considered qubit. In Step 3, determine how to proceed based on the index of the currently considered qubit within its set. If that qubit is the first element of its set, proceed to Case I; if it is the second, proceed to Case II; otherwise, proceed to Case III. Case I: save the orthonormalized vectors spanning the subspace constructed in Step 2. Some linear combination of those vectors will yield a power-optimal pulse shape for the currently considered qubit. Case II: using two sets of orthonormal vectors, for the currently considered and the immediately preceding qubits, compute the power-optimal pulse shapes for those qubits given their interaction matrix. Case III: Compute the pulse shape for the currently considered qubit that satisfies the desired entangling interactions between itself and all of the previously considered qubits. We iterate Steps 1–3 until all participating qubits have been accounted for. This method may be used for non-overlapping or overlapping pairs of qubits. See Supplementary Note 2 for further details.