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

Sven Jandura and Guido Pupillo

University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France

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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 Ansätze 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.

In this work we apply quantum optimal control techniques to optimize quantum gates on Rydberg atoms. We find the shortest possible global laser pulse to implement at CZ and a C$_2$Z gate in the blockade regime. We show how to adapt the pulses to compensate for a finite Rydberg blockade strength and how to minimize the time spent in the Rydberg state instead of the pulse duration.

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Cited by

[1] K. McDonnell, L. F. Keary, and J. D. Pritchard, "Demonstration of a Quantum Gate using Electromagnetically Induced Transparency", arXiv:2204.03733.

[2] Daniel González-Cuadra, Torsten V. Zache, Jose Carrasco, Barbara Kraus, and Peter Zoller, "Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms", arXiv:2203.15541.

[3] Christiane P. Koch, Ugo Boscain, Tommaso Calarco, Gunther Dirr, Stefan Filipp, Steffen J. Glaser, Ronnie Kosloff, Simone Montangero, Thomas Schulte-Herbrüggen, Dominique Sugny, and Frank K. Wilhelm, "Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe", arXiv:2205.12110.

[4] Alice Pagano, Sebastian Weber, Daniel Jaschke, Tilman Pfau, Florian Meinert, Simone Montangero, and Hans Peter Büchler, "Error-budgeting for a controlled-phase gate with strontium-88 Rydberg atoms", arXiv:2202.13849.

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