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

TL;DR

This paper develops time-optimal laser pulses for implementing high-fidelity controlled-Z and C2Z gates in Rydberg atoms, simplifying experimental procedures and mitigating errors through quantum optimal control techniques.

Contribution

It introduces a method to design smooth, time-optimal laser pulses for multi-qubit gates in Rydberg atoms, reducing complexity and error susceptibility.

Findings

Achieved theoretical gate fidelities compatible with error correction.

Designed global laser pulses that do not require single-site addressability.

Mitigated errors due to finite Rydberg state lifetime and blockade strength.

Abstract

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 Ans\"atze 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.