Photon-number-selective two-excitation transitions for bosonic quantum error correction*

Single-photon loss is the dominating source of error in bosonic quantum error correcting codes using microwave resonators. To correct for this type of error, we can use code words of one defined parity (such as cat states or binomial states). Using an ancilla qubit dispersively coupled to a high quality resonator, we propose to realize a collection of photon-number-selective simultaneous single excitations on both the resonator and the qubit.  These transitions are implemented by driving the system with a comb of microwave tones and serve a double purpose. By applying them, we can simultaneously detect the presence of an error and move back to the code space.

Being number-selective, these drives do not affect the code states so they can be applied whether an error has happened or not. We present the experimental implementation of the drives and the phase control they enable on superpositions of Fock states. When supplemented by qubit reset, the presented sequence is suitable for quantum error correction of against single-photon loss.