Achieving Negative Dispersive Shift Matching for Fault Tolerant Error Mapping in Pair Coherent States.*

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 to avoid storage lifetime degradation, as an ancilla due to the large anharmonicity. This allows practical use of the straddling regime of the qubit spectrum to produce negative chi matching on the two modes.

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

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