Multiqubit Rydberg Gates for Quantum Error Correction

PRX Quantum, vol. 7

Abstract

Multiqubit gates that involve three or more qubits are usually thought to be of little significance for fault-tolerant quantum error correction because single gate faults can lead to errors of high Pauli weight. However, recent works have shown that multiqubit gates can be beneficial for measurement-free fault-tolerant quantum error correction and for fault-tolerant stabilizer readout in unrotated surface codes. In this work, we investigate multiqubit Rydberg gates that are useful for fault-tolerant quantum error correction in single-species neutral-atom platforms and can be implemented with global laser pulses that do not individually address atomic sites. We develop an open-source Python package to generate analytical, few-parameter pulses that implement the desired gates while minimizing gate errors due to Rydberg-state decay. The tool also allows us to identify parameter-optimal pulses, characterized by a minimal parameter count for the pulse ansatz. Measurement-free quantum error correction protocols require controlled-controlled-Z (CCZ) gates, which we analyze for atoms arranged in symmetric and asymmetric configurations. We investigate the performance of these schemes for various single-, two-, and three-qubit gate error rates, showing that break-even performance of measurement-free quantum error correction is within reach of current hardware. Moreover, we study Floquet quantum error correction protocols that comprise two-body stabilizer measurements. Those can be realized using global three-qubit gates, and we show that this can lead to a significant reduction in shuttling operations. Simulations with realistic circuit-level noise indicate that applying three-qubit gates for stabilizer measurements in Floquet codes can yield competitive logical qubit performance in experimentally relevant error regimes.

Authors 7

1. David F. Locher Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Forschungszentrum Jülich

   RWTH Aachen University

2. Josias Old Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Forschungszentrum Jülich

   RWTH Aachen University

3. Katharina Brechtelsbauer

   University of Stuttgart

   Affiliation as printed

   University of Stuttgart

4. Jakob Holschbach Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Forschungszentrum Jülich

   RWTH Aachen University

5. Hans Peter Büchler

   University of Stuttgart

   Affiliation as printed

   University of Stuttgart

6. Sebastian Weber

   University of Stuttgart

   Affiliation as printed

   University of Stuttgart

7. Markus Müller Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Forschungszentrum Jülich

   RWTH Aachen University