Continuous Quantum Gate Sets and Pulse-Class Meta-Optimization

In the context of quantum computing gate-synthesis and control problems present a vast range of external parameter dependencies, both physical and application specific. These parameters may represent e.g. Hamiltonian-specific terms, which drift in time or vary significantly from one system to another, or alternatively different gate configurations and even specific experimental parameters such as those describing e.g. filter and transfer functions. In this work, we address the possibility of learning families of optimal-control pulses that depend adaptively on various parameters, in order to obtain a global optimal mapping from the space of potential parameter values to the control space and hence to produce continuous classes of gates. We test our algorithms on different experimentally relevant quantum gates in the context of superconducting quantum circuits and show how we can construct high-fidelity pulses even in the presence of multiple variables or uncertain parameters with wide ranges. We also discuss and simulate different possible direct applications of our methods to experiments.