Fast Sideband Control of a Multimode Cavity Memory with Weak Dispersive Coupling to a Transmon

Mitigating ancilla-mediated error channels is a critical challenge in controlling high-quality superconducting cavities using circuit quantum electrodynamics (cQED). We address this by weakening the dispersive coupling while demonstrating fast, high-fidelity multimode control through transmon-mediated sideband interactions. We implement transmon-cavity SWAP gates with speeds up to 30 times larger than the bare dispersive coupling. Combined with transmon rotations, this enables universal state preparation in a single mode, though achieving unitary gates and extending control to multiple modes remains a challenge. In this work, we overcome this limitation by introducing two control strategies: (i) a shelving technique that stores populations in sideband-transparent states, and (ii) a method that exploits the dispersive shift to implement photon-number-selective transmon-cavity SWAP gates. We use these protocols to prepare Fock and binomial code states across any of the ten modes of a multimode cavity with millisecond coherence times—serving as a multimode quantum memory. We demonstrate unitaries that encode and decode an arbitrary qubit state from the transmon into corresponding vacuum and Fock state superpositions, as well as entangled NOON states of cavity mode pairs—a scheme extendable to arbitrary multimode Fock encodings in the cavity modes. Furthermore, we implement a new binomial encoding gate that converts arbitrary transmon superpositions into binomial code states in any cavity mode at a rate exceeding the dispersive shifts in our system, achieving an average post-selected state fidelity of 96.3% in a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>4</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi mathvariant="normal">μ</a:mi> <a:mi mathvariant="normal">s</a:mi> </a:mrow> </a:math> gate time. By using precalibrated transmon and sideband pulses, our work demonstrates multimode control with significantly reduced calibration overhead, enabling efficient unitary operations using sideband interactions in multimode cQED systems.