Optical integrated quantum computing protocols, in particular using the dual-rail encoding, require that waveguides cross each other to realize, e.g., SWAP or Toffoli gate operations. We demonstrate efficient adiabatic crossings. The working principle is explained using simulations, and several test circuits are fabricated in silicon nitride (SiN) to characterize the coupling performance and insertion loss. Well-working crossings are found by experimentally varying the coupler parameters. The adiabatic waveguide crossing (WgX) outperforms a normal directional coupler in terms of spectral working range and fabrication variance stability. The insertion loss is determined using two different methods: using the transmission and by incorporating crossings in microring resonators. We show that the latter method is very efficient for low-loss photonic components. The lowest insertion loss is 0.18 dB (4.06%) enabling high-fidelity NOT operations. The presented WgX represents a high-fidelity (96.2%) quantum NOT operation.