Strategies and trade-offs for controllability and memory time of microwave cavities in circuit QED: part II

Three-dimensional microwave cavity resonators have been shown to reach lifetimes of the order of a second by careful design and fabrication. Such cavities represent an ideal platform for quantum computing with bosonic qubits, but their efficient control remains an outstanding problem since the large mode volume results in inefficient coupling to nonlinear elements used for their control. Moreover, this coupling induces additional cavity dissipation which can easily destroy the advantage of long intrinsic lifetime. Here, we discuss conditions on, and protocols for, efficient control of these ultra-high-quality microwave cavities using conventional nonlinear circuits. We show that, surprisingly, controlling ultra-high-Q cavities does not require similar quality factors for the auxiliary qubits used to control them. Our work explores a potentially viable roadmap towards using ultra-high-quality microwave cavity resonators for storing and processing information encoded in bosonic qubits. In part II, I will talk about our numerical simulations, which demonstrate that efficient control and measurements of cavities with second-scale lifetime is possible with state-of-the-art transmon devices and outline a route towards controlling cavities with even higher quality factors.