High-fidelity quantum gate learning via physics-informed neural networks

We propose a physics-informed neural network (PINN) approach for high-fidelity quantum gate learning in both one- and two-qubit systems. We train a PINN using the time-dependent Schrödinger equation, where smooth control fields with fixed boundary conditions are obtained by minimizing a loss function that considers model dynamics, gate error, physical constraints, regularization terms, and multiple initial conditions. Training considers pairs of mutually unbiased bases, while independent validation combines Haar-random input states with the average gate fidelity. Unitary simulations yield an average gate infidelity of $8.49\times10^{-8}$ for Hadamard and values between $3.39\times10^{-7}$ and $4.96\times10^{-6}$ for controlled-NOT under $XX$, $YY$, and $ZZ$ interactions. We examine how the learned control fields depend on the coupling, training configuration, and available local fields, including five exchange-type dipolar scenarios. We test the learned control fields under the Lindblad master equation with dephasing and amplitude damping, theoretically reproducing the expected first-order fidelity loss in the weak-dissipation regime. Finally, boundary-adapted Chebyshev expansions represent 139 learned controls with a minimum common count of $K_\ast=24$ coefficients per control for all eleven family-averaged mean squared errors to fall below $10^{-6}$. Separately, square-pulse and Strang propagation at $K=30$ preserve all 31 continuous polynomial references within infidelity $10^{-5}$ at $N=128$ and all larger tested resolutions, under both sampling rules. These results connect multi-state gate synthesis, control-resource characterization, and compact square-pulse playback.