Universal control of an oscillator with dispersive coupling to a qubit

We investigate quantum control of an oscillator mode off-resonantly coupled to an ancillary qubit. In the strong dispersive regime, we may drive the qubit conditioned on the number states of the oscillator, which, together with displacement operations, can achieve universal control of the oscillator. Based on our proof of universal control, we provide a straightforward recipe to perform arbitrary unitary operations on the oscillator. With the capability of universal control, we can significantly reduce the number of operations to prepare the number state vertical bar n > from O(n) to O(root n). This universal control scheme of the oscillator enables us to efficiently manipulate the quantum information stored in the oscillator, which can be implemented using superconducting circuits.