Parametrized multiqubit gate design for neutral-atom based quantum platforms

Abstract: 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 $N \geq 2$). 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 $\mathrm{C_1P}$ and $\mathrm{C_2P}$ 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. Further, 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.