Transmon-mediated gates on GKP qubits in superconducting circuits – Part 1

Recent experimental results of quantum error correction (QEC) extending the lifetime of qubits encoded in Gottesman-Kitaev-Preskill (GKP) codes have shown the great potential of these bosonic codes as a hardware-efficient approach for fault tolerant quantum computing [1, 2]. Demonstrating logical gates is now key for enabling the ability to perform quantum algorithms with GKP qubits. Here, we discuss theoretical predictions on the performance of logical GKP single- and two-qubit gates based on the current proposed scheme in the superconducting architecture, where a physical qubit rotation of an auxiliary is applied to mediate the gate on the GKP qubit [3].

[1] Sivak, V.V., Eickbusch, A., Royer, B. et al. Real-time quantum error correction beyond break-even. Nature 616, 50–55 (2023).

[2] Lachance-Quirion, D., Lemonde, M. et al. Autonomous Quantum Error Correction of Gottesman-Kitaev-Preskill States. Phys. Rev. Lett. 132, 150607 (2024)

[3] Singh S. (2023, November 12). 4.7 Shraddha Singh [Video]. YouTube. https://www.youtube.com/watch?v=2DRORDLQWsk