  Room temperature single-photon sources (SPSs) are critical for the emerging
practical quantum applications such as on-chip photonic circuity for quantum
communications systems and integrated quantum sensors. However, direct
integration of an SPS into on-chip photonic systems remains challenging due to
low coupling efficiencies between the SPS and the photonic circuitry that often
involve size mismatch and dissimilar materials. Here, we develop an adjoint
topology optimization scheme to design high-efficiency couplers between a
photonic waveguide and SPS in hexagonal boron nitride (hBN). The algorithm
accounts for fabrication constraints and the SPS location uncertainty. First, a
library of designs for the different positions of the hBN flake containing an
SPS with respect to a Si$_{3}$N$_{4}$ waveguide is generated, demonstrating an
average coupling efficiency of 78%. Then, the designs are inspected with
dimensionality reduction technique to investigate the relationship between the
device geometry (topology) and performance. The fundamental, physics-based
intuition gained from this approach could enable the design of high-performance
quantum devices
