Pulse family optimization for parameterized quantum gates using spectral clustering

Parameterized gate circuits are used in many applications in the current Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing. These parameterized gates are mainly implemented using analytically found pulse protocols, often yielding suboptimal gate times, and consequently, fidelities. Alternatively, gate optimization algorithms are designed to construct high-fidelity pulses for individual fixed points in a continuous parameter space. Gates for intermediate parameters can subsequently be found by some form of interpolation between previously constructed pulses. Nevertheless, it is not guaranteed (as with analytic protocols) that the pulses found by the optimization algorithms belong to the same family of solutions and thus resemble each other. Interpolation of two pulses from different solution families often leads to high infidelities, as the pulse strays away from the minimum in the parameter/fidelity landscape. This work introduces a spectral clustering method to sort high-fidelity, optimized pulses in families and interpolate solely between pulses of the same family. Accordingly, interpolations will always approach maximal fidelity. Furthermore, as more than one pulse family is constructed, the parameter space can be partitioned, and according to this partition, a family prevails fidelity-wise. This work provides a meticulous demonstration of our constitutive continuous gate family construction by applying it to a universal gate set for Rydberg and Cat qubits under noise.