  Bosonic modes have wide applications in various quantum technologies, such as
optical photons for quantum communication, magnons in spin ensembles for
quantum information storage and mechanical modes for reversible
microwave-to-optical quantum transduction. There is emerging interest in
utilizing bosonic modes for quantum information processing, with circuit
quantum electrodynamics (circuit QED) as one of the leading architectures.
Quantum information can be encoded into subspaces of a bosonic superconducting
cavity mode with long coherence time. However, standard Gaussian operations
(e.g., beam splitting and two-mode squeezing) are insufficient for universal
quantum computing. The major challenge is to introduce additional nonlinear
control beyond Gaussian operations without adding significant bosonic loss or
decoherence. Here we review recent advances in universal control of a single
bosonic code with superconducting circuits, including unitary control, quantum
feedback control, driven-dissipative control and holonomic dissipative control.
Entangling different bosonic modes with various approaches is also discussed.
