Neural-network-based design and implementation of fast and robust quantum gates

Abstract: We present a continuous-time, neural-network-based approach to optimal control in quantum systems, with a focus on pulse engineering for quantum gates. Leveraging the framework of neural ordinary differential equations, we construct control fields as outputs of trainable neural networks, thereby eliminating the need for discrete parametrization or predefined bases. This allows for generation of smooth, hardware-agnostic pulses that can be optimized directly using differentiable integrators. As a case study we design, and implement experimentally, a short and detuning-robust $\pi/2$ pulse for photon parity measurements in superconducting transmon circuits. This is achieved through simultaneous optimization for robustness and suppressing the leakage outside of the computational basis. These pulses maintain a fidelity greater than $99.9\%$ over a detuning range of $\approx \pm 20\mathrm{MHz}$, thereby outperforming traditional techniques while retaining comparable gate durations. This showcases its potential for high-performance quantum control in experimentally relevant settings.