Fast sideband control of a multimode bosonic memory with a weakly coupled transmon ancilla

High-Q 3D multimode cavities coupled to nonlinear ancillary circuits are a promising platform for quantum computing. This architecture has the advantages of long cavity coherence times and the ability to realize multiplexed control of a register of cavity modes with only a few control lines. Critical challenges for this architecture include crosstalk errors that emerge from the always-on dispersive interaction, ancilla decoherence and backaction on cavity states, and fundamental limits on cavity mode coherence times due to the inverse Purcell effect.

In this work, we mitigate these errors by weakening the coupling between the cavity and transmon. While this typically lowers gate speeds in standard dispersive control protocols, we achieve fast transmon-cavity SWAP gates—25 times faster than the bare dispersive rate—by using charge-driven (f,n-g,n+1) sideband interactions. This realizes a tunable Jaynes-Cummings interaction controlled by ancilla displacements which, in conjunction with transmon rotations, enables arbitrary multimode state preparation. Here, we extend the standard Law-Eberly paradigm to demonstrate control schemes based on state shelving that can be used to encode logical qubits in arbitrary pairs of multimode Fock states. We use this method to prepare binomial code states across ten modes and encode NOON states in arbitrary pairs of modes. We also realize a broader range of unitary gates by leveraging the residual dispersive shift to match sideband transition rates across different photon-numbers, which we use to implement a fast binomial encoding unitary with a gate time shorter than the dispersive shift. We explore the speed and fidelity limits of (f,n-g,n+1) sideband SWAP gates, applicable more broadly to transmon charge-driven interactions.