Three-dimensional microwave cavity resonators have been shown to reach lifetimes of the order of a second by maximizing the cavity volume relative to its surface, using better materials,and improving surface treatments. 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 decay via the inverse Purcell effect which can easily destroy the advantage of {a} long intrinsic lifetime. Here, we discuss conditions on, and protocols for, efficient utilization of these ultra-high-quality microwave cavities as memories for conventional superconducting qubits. We show that, surprisingly, efficient write and read operations with ultra-high-quality cavities does not require similar quality factors for the qubits and other nonlinear elements used to control them. Through a combination of analytical and numerical calculations, we demonstrate that efficient coupling to cavities with second-scale lifetime is possible with state-of-the-art transmon and SNAIL devices and outline a route towards controlling cavities with even higher quality factors. 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 hybrid circuit QED architectures containing both ancilla qubits and bosonic modes, a controlled beam splitter gate is a powerful resource. It can be used to create (up to a controlled-parityoperation) an ancilla-controlled SWAP gate acting on two bosonic modes. This is the essential element required to execute the `swap test‘ for purity, prepare quantum non-Gaussian entanglement and directly measure nonlinear functionals of quantum states. It also constitutes an important gate for hybrid discrete/continuous-variable quantum computation. We propose a new realization of a hybrid cSWAP utilizing `Kerr-cat‘ qubits — anharmonic oscillators subject to strong two-photon driving. The Kerr-cat is used to generate a controlled-phase beam splitter (cPBS) operation. When combined with an ordinary beam splitter one obtains a controlled beam-splitter (cBS) and from this a cSWAP. The strongly biased error channel for the Kerr-cat has phase flips which dominate over bit flips. This yields important benefits for the cSWAP gate which becomes non-destructive and transparent to the dominate error. Our proposal is straightforward to implement and, based on currently existing experimental parameters, should achieve controlled beam-splitter gates with high fidelities comparable to current ordinary beam-splitter operations available in circuit QED.
The Mach–Zehnder interferometer is a powerful device for detecting small phase shifts between two light beams. Simple input states — such as coherent states or single photons— can reach the standard quantum limit of phase estimation while more complicated states can be used to reach Heisenberg scaling; the latter, however, require complex states at the input of the interferometer which are difficult to prepare. The quest for highly sensitive phase estimation therefore calls for interferometers with nonlinear devices which would make the preparation of these complex states more efficient. Here, we show that the Heisenberg scaling can be recovered with simple input states (including Fock and coherent states) when the linear mirrors in the interferometer are replaced with controlled-swap gates and measurements on ancilla qubits. These swap tests project the input Fock and coherent states onto NOON and entangled coherent states, respectively, leading to improved sensitivity to small phase shifts in one of the interferometer arms. We perform detailed analysis of ancilla errors, showing that biasing the ancilla towards phase flips offers a great advantage, and perform thorough numerical simulations of a possible implementation in circuit quantum electrodynamics. Our results thus present a viable approach to phase estimation approaching Heisenberg-limited sensitivity.