Towards two-mode bosonic quantum error correction with the pair cat code

The stabilization of Bosonic qubits in microwave cavities is a promising step towards implementing quantum error correction codes. The pair cat code, which utilizes a two-mode entangled state, assures significant advantages over the previously implemented one-mode cat code for autonomous quantum error correction schemes [1]. A pair coherent state (PCS) forms the basis of this pair cat code where the error syndrome can be measured from the photon number difference (PND) between the two modes [2]. Measuring the PND of the system can be made first order fault tolerant by achieving negative matching of the dispersive shift values for the two storage modes. We achieve this by utilizing a fluxonium qubit, with a local flux application in a 3D architecture with quasi-planar storage modes. An external drive is used to fine tune the dispersive shifts to achieve an exact negative matching value. Utilizing FWM processes, we generate binomial variants of the pair cat code and perform an error correction cycle on this two-mode code to correct for single photon loss.

[1] V. V. Albert et al., Quantum Sci. Technol. 4, 035007 (2019).

[2] J. M. Gertler et al., PRX Quantum 4, 020319 (2023).