Fidelity-informed neural pulse compilation of a continuous family of quantum gates with uncertainty-margin analysis

We develop a fidelity-informed neural pulse-compilation framework for a continuous family of single-qubit gates on a three-qubit liquid-state nuclear magnetic resonance (NMR) processor. Instead of decomposing each target unitary into a sequence of calibrated basis gates, the method learns a direct map from the axis-angle parameters of an arbitrary U_2 in SU(2) operation to a piecewise-constant radio-frequency control sequence that implements the desired transformation. Training is performed end-to-end through the time-ordered propagator of the driven Hamiltonian using global-phase-insensitive unitary fidelity as the learning signal. We show numerically that a single model generalizes across a continuous range of gate parameters and experimentally validate representative compiled pulses on a benchtop three-qubit NMR device. In addition, we analyze sensitivity to structured perturbations in Hamiltonian and control parameters by introducing a prescribed uncertainty set and performing a comparative risk-aware redesign based on right-tail Conditional Value-at-Risk (RU-CVaR). This stage produces pulse solutions with broader tolerance margins within the chosen uncertainty model. The results demonstrate continuous pulse-level gate synthesis in an experimentally accessible setting and illustrate a hardware-aware compilation strategy that can be extended to other quantum platforms. While the uncertainty model considered here is tailored to NMR, the neural compilation and risk-aware optimization framework are general and may be useful in architectures where calibration overhead, parameter drift, or control constraints make repeated per-gate optimization costly.