Figure 3

Selective broadcasting schemes for simultaneous single-qubit control of multiple qubits. Main figure: Example of a single Clifford round for n=2 qubits targeting C₂ (C₁₃) in Q_T (Q_B) (C_j defined in Supplementary Material at [http://www.nature.com/npjqi]). In the sequential scheme, the pulses implementing C₂ are directed to Q_T, after which the pulses implementing C₁₃ are directed to Q_B. In the compiled scheme, the two Cliffords are realised concurrently using a pre-determined pulse sequence, with appropriate markers, which minimises the total number of pulses, N_p (see Supplementary Material at [http://www.nature.com/npjqi] for additional data on the compilation algorithm). Finally, in the five-primitives scheme, a fixed sequence of five pulses is repeated in each round (N_p=5). The targeted Cliffords are then applied simultaneously by selecting the appropriate subset of pulses for each qubit (see Supplementary Material at [http://www.nature.com/npjqi] for additional data on the five-primitives marker table). Top-right: scaling of the average pulses per multiqubit combination of Cliffords, 〈N_p〉, versus qubit number n. The constant scaling achieved by the five-primitives scheme provides a dramatic improvement over the linear scaling of the sequential scheme. Although 〈N_p〉 is always lowest for the compiled scheme, pre-compiling the optimal pulse and marker combinations is impractical for n≳5, and the improvement over the simpler five-primitives scheme is negligible by n~10.