Conditional Displacement control of an oscillator with a fluxonium ancilla

Redundantly encoding logical information in the infinite-dimensional Hilbert space of a single oscillator offers a hardware-efficient route to quantum error correction. Oscillators being linear systems, universal control is typically achieved by combining with a qubit ancilla that provides the required nonlinearity [1]. However, ancilla errors circulating back to the storage cavity can degrade the logical information. Echoed Conditional Displacement (ECD) gate which enables universal control of a cavity is robust against dephasing and sensitive to qubit relaxation. Therefore a noise-biased ancilla replacing transmon can potentially yield better control fidelities. The double well potential landscape of fluxonium makes it resilient to bit-flip, adding an extra layer of protection against errors stemming from the ancilla itself. This comes at the expense of increased decoherence in fluxonium to which ECD protocol is less sensitive to nevertheless. The asymmetry in qubit noise compatible with ECD requirements makes fluxonium an ideal candidate for bosonic circuits. We numerically verify increased gate fidelities in fluxonium-cavity gates and explore mechanisms that fundamentally limit how far can gate fidelities be pushed. We compare the gate performance of traditional transmon-assisted ECD gates replaced with protected fluxonium ancilla for their integration in bosonic code architectures.

[1] Eickbusch, A., Sivak, V., Ding, A.Z. et al. Fast universal control of an oscillator with weak dispersive coupling to a qubit. Nat. Phys. 18 (2022).