  Bosonic encoding is an approach for quantum information processing, promising
lower hardware overhead by encoding in the many levels of a harmonic oscillator
mode. Scaling to multiple modes requires weak interaction for independent
control, yet strong interaction for fast control. Applying fast and efficient
universal control on multiple modes remains an open problem. Surprisingly, we
find that displacements conditioned on the state of a single qubit ancilla
coupled to multiple harmonic oscillators are sufficient for universal control.
We present the conditional-no operation concept, which can be used for reducing
the duration of entangling gates. Within this guiding concept, we develop the
conditional not displacement control method which enables fast generation and
control of bosonic states in multi-mode systems weakly coupled to a single
ancilla qubit. Our method is fast despite the weak ancilla coupling. The weak
coupling in turn allows for excellent separability and thus independent
control. We demonstrate our control on a superconducting transmon qubit weakly
coupled to a multi-mode superconducting cavity. We create both entangled and
separable cat-states in different modes of the multi-mode cavity, showing
entangling operations at low cross-talk while maintaining independent control
of the different modes. We show that the operation time is not limited by the
inverse of the coupling rate, which is the typical timescale, and we exceed it
by almost 2 orders of magnitude. We verify our results with an efficient method
for measurement of the multi-mode characteristic function which employs our
conditional not displacement. Our results inspire a new approach toward general
entangling operations and allow for fast and efficient multi-mode bosonic
encoding and measurement.
