Ancilla-fault tolerant control of linear quantum memories with dynamic dispersive coupling

Superconducting resonators offer a rich playground for continuous-variable quantum simulations, computation, and error correction. In isolation, these resonators are linear and only suffer a single correctible error (photon loss), making them potential quantum memories. There has been much progress towards controlling these memories by dispersively coupling them to ancillary superconducting qubits, but this introduces non-linearity and dephasing to the memories, and control fidelity is often limited by the ancilla qubit's decoherence. We introduce a novel architecture that breaks this trade-off, by inserting a quasi-linear coupler between the memories and the qubit. This 'Linear INductive Coupler' (LINC), a novel three-wave mixing element that is linear when undriven, ensures that the inherited non-linearity and dephasing of the memories are both much smaller than their linewidths. Gaussian control of the memories, like beamsplitting and squeezing, is directly enabled by parametrically driving the LINC. When non-Gaussian control or tomography is required, the LINC can activate a dynamic dispersive coupling between the memory and the ancilla qubit, similar to other recent proposals [1]. We further show that full parametric control of the memory-qubit interaction enables first-order tolerance to both decay and low-frequency dephasing of the qubit, achieving universal control limited only by the memories' long lifetimes.