Parametrized multiqubit gates for neutral-atom quantum platforms

A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer from various sources of error that propagate with the circuit depth. Parametrized gates in particular have found use in both near-term algorithms and circuit compilation. The one- and two-qubit versions of these gates have been demonstrated on various computing architectures. The neutral-atom platform has the capability to implement native $N$-qubit gates (for $N\ensuremath{\ge}2$). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls---laser pulses to excite an atom to Rydberg states---that implement phase gates with one and two controls, the ${\mathrm{C}}_{1}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}$ and ${\mathrm{C}}_{2}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}$ gates, respectively, on neutral-atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. In addition, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral-atom hardware.