Efficient cavity control with SNAP gates

Microwave cavities coupled to superconducting qubits have been demonstrated to be a promising platform for quantum information processing. A major challenge in this setup is to realize universal control over the cavity. A promising approach are selective number-dependent arbitrary phase (SNAP) gates combined with cavity displacements. Whereas it could be proven that this is a universal gate set, a central question remained open: how can a given target operation be realized efficiently with a sequence of these operations.

In this talk, we present a practical scheme to address this problem. We will compare our results to previously known techniques: for many experimentally relevant applications, we find that the sequence length can be reduced by a factor of around 10 or higher. We will also sketch the working principle of our method.