Efficient simulations of Lindblad master equations in the stabilized code space of cat qubits

We introduce a new method to obtain effective reduced dynamics on the decoherence-free subspace of a dissipative Lindblad dynamics having multiple degenerate steady states.

This method relies on the asymptotic expansion of the perturbative dynamics (usually modelling decoherence channels, or the effect of imperfect gate implementations) in the Heisenberg picture; which is particularly well adapted to the study of composite systems with multiple cat qubits stabilized by a strong two-photon dissipative mechanism.

We illustrate the advantages of this method by explicitly showing how to apply it to the simulation of multi-cat qubit gates; which was a previously intractable numerical problem.