Time-Optimal Two- and Three-Qubit Gates for Rydberg Atoms*

Entangling gates between two or more qubits stored in the electronic states of neutral atoms can be implemented via the strong and long-range interaction of atoms in highly excited Rydberg states. Two properties of a gate are particularly desirable: Firstly, the gate should be fast, since many types of error can be mitigated by short gate durations. Secondly, it should be implemented by a global laser pulse which does not require single site addressability of the atoms, simplifying experimental implementation of the gate. In this work we use two quantum optimal control techniques, gradient ascent pulse engineering (GRAPE) and Pontryagins’s maximum principle, to determine time-optimal global laser pulses implementing a controlled-Z(CZ) gate and a three qubit C₂Z gate. Our pulses improve upon the traditional non-global pulses for the CZ and the C₂Z gate with just a limited set of variational parameters, demonstrating the potential of quantum optimal control techniques for advancing quantum computing with Rydberg atoms.