Quantum error mitigation for GKP qubits

In recent years, a plethora of quantum error mitigation techniques have been proposed to undo errors in currently available quantum devices.

While these techniques are not a substitute for a fault-tolerant quantum computer, as they are ultimately unscalable, they are still believed to play

an important role for intermediate-scale devices. Most of these techniques have been developed for the case of qubits, while little has been done

for other quantum systems such as continuous variable systems.

Recent works have also explored the application of error mitigation techniques together with error correction [1, 2, 3]. In this talk, we extend these ideas

to the continuous variable case and, in particular, to the Gottesman-Kitaev-Preskill (GKP) code [4]. Focusing mostly on the technique of

probabilistic error cancellation via quasiprobability decompositions, we show how to obtain such decompositions in the continuous-variable case

in order to undo coherent and incoherent noise in the quantum state. We also provide a comparison with the simple qubit case

for different noise levels.

[1] M. Lostaglio & A. Ciani, Phys. Rev. Lett. 127, 200506 (2021)

[2] C. Piveteau, D. Sutter, S. Bravyi, J. M. Gambetta & K. Temme, Phys. Rev. Lett. 127, 200505 (2021)

[3] Y. Suzuki, S. Endo, K. Fujii & Y. Tokunaga, PRX Quantum 3, 010345 (2022)

[4] D. Gottesman A. Kitaev & John Preskill Phys. Rev. A 64, 012310 (2001)