arXiv2025
Realizing the promise of quantum computing requires simultaneously increasing Hilbert-space size and coherence times. While qubit-based architectures have long been the dominant paradigm, large local Hilbert spaces enable qudits, which offer more compact circuits and natural representations for quantum simulation in chemistry, condensed matter, and high-energy physics. Superconducting radio-frequency (SRF) cavities are attractive building blocks for qudit-based quantum technologies because of their exceptionally low dissipation and large bosonic Hilbert spaces, but turning them into programmable modules requires extra effort because the nonlinear circuitry required for control and measurement often introduces loss and noise that erode the memory advantage. Here we demonstrate a two-mode SRF cavity module weakly coupled to an ancillary transmon circuit and engineered to suppress controller-induced dissipation and dephasing, achieving single-photon lifetimes of 20.6 ms and 15.6 ms and a dephasing time exceeding 40 ms. Using sideband interactions together with error-resilient protocols incorporating measurement-based correction and post-selection, we prepare Fock states up to $N=20$ with fidelities exceeding 95% and generate two-mode entanglement near the coherence limit, approaching 99.9%. By combining ultracoherent storage with high-fidelity control, this work moves cavity-based hardware beyond memory-only operation and establishes a practical route toward high-dimensional encodings and scalable modular quantum information processing.