Loss channel analysis of cat qubit circuits

Cat qubits are bosonic quantum error correcting codes that have noise bias: they suppress bit-flip errors exponentially at the cost of a linear increase of phase-flip errors. In current dissipative cat-qubit designs, autonomous correction of bit-flips is achieved by parametrically activating a four-wave mixing interaction, whose amplitude determines the confinement rate to the code space. This rate also sets an upper bound to the speed of the gates required to detect and correct phase-flip errors with a repetition code, for instance. However, for this approach to be relevant, the phase-flip error rate should not be affected by the parametric processes. This presentation will use time-dependent perturbation theory, and numerically exact Floquet methods, to quantify parametrically-activated spurious relaxation processes.