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

We identify time-optimal laser pulses to implement the controlled-Z gate and its three-qubit generalization, the C(2)Z gate, for Rydberg atoms in the blockade regime. Pulses are optimized using a combination of numerical and semi-analytical quantum optimal control techniques that result in smooth Ansatze with just a few variational parameters. For the CZ gate, the time-optimal implementation corresponds to a global laser pulse that does not require single-site addressability of the atoms, simplifying experimental implementation of the gate. We employ quantum optimal control techniques to mitigate errors arising due to the finite lifetime of Rydberg states and finite blockade strengths, while several other types of errors affecting the gates are directly mitigated by the short gate duration. For the considered error sources, we achieve theoretical gate fidelities compatible with error correction using reasonable experimental parameters for CZ and C(2)Z gates.

Automated summary

In this study, we identify time-optimal laser pulses for implementing the controlled-Z gate and its generalization, the C(2)Z gate, for Rydberg atoms. The pulses are optimized using quantum optimal control techniques, resulting in smooth waveforms with only a few variational parameters. The short gate duration helps mitigate errors while achieving theoretical gate fidelities compatible with error correction.