Fig. 3: Experimental results of nonlinear interactions in vortex systems.

a Trajectories of vortex particles obtained from ideal (noiseless) simulation, noisy simulation, and experimental data. b Fidelity and the position deviations as functions of time. The fidelity F at each time step t is defined as \(F=| \langle {\psi }_{{{\rm{ideal}}}}^{t}| {\psi }_{{{\rm{exp}}}}^{t}\rangle {| }^{2}\), where \(|{\psi }_{{{\rm{exp}}}}^{t}\rangle\) and \(|{\psi }_{{{\rm{ideal}}}}^{t}\rangle\) denote the state vector of the spatial qubits obtained through experiment and noiseless numerical simulation, respectively. The position deviation is defined as the Euclidean distance between the vortex particles in the experiment and that in noiseless simulation \(d={\sum }_{n=1}^{{N}_{p}}| {\vec{r}}_{{{\rm{exp}}}}^{n,t}-{\vec{r}}_{{{\rm{ideal}}}}^{n,t}|\), where \({\vec{r}}_{{{\rm{exp}}}}^{n,t}\) and \({\vec{r}}_{{{\rm{ideal}}}}^{n,t}\) denote the coordinates of the vortex particle n at time t obtained through experiment and noise-free simulation, respectively. c, d Velocity fields and streamlines induced by vortex particles at t = 24, 44, 62, and 81, obtained in the experiment (c) and noiseless simulation (d).