Conditional not displacement: fast multi-oscillator control with a single qubit

Bosonic encoding is an approach for quantum information processing, promising lower hardware overhead by encoding in the many levels of a harmonic oscillator. Scaling to multiple modes requires them to be decoupled for independent control, yet strongly coupled for fast interaction. How to perform fast and efficient universal control on multiple modes remains an open problem. We develop a control method that enables fast multi-mode generation and control of bosonic qubits which are weakly coupled to a single ancilla qubit. The weak coupling allows for excellent independent control, despite the weak ancilla coupling our method allows for fast control. We demonstrate our control by using a superconducting transmon qubit coupled to a multi-mode superconducting cavity. We create both entangled and separate cat-states in different modes of a multi-mode cavity, showing the individual and coupled control of the modes. We show that the operation time is not limited by the inverse of the dispersive coupling rate, which is the typical timescale, and we exceed it in practice by almost 2 orders of magnitude. Our scheme allows for multi-mode bosonic codes as well as more efficient scaling of hardware.