Dual-rail encoding in a fixed-frequency multimode transmon qubit with ancilla-free erasure error-detection

Amplitude damping errors are a dominant source of error in high performance quantum processors. A promising approach in error-detection are “erasure qubits”, where amplitude damping errors are converted into detectable leakage outside of the computational subspace. Dual-rail encoding has been demonstrated in superconducting quantum devices to show extended coherence above that of the constituent elements, however, these architectures can require the use of an ancillary qubit to perform the erasure error detection. Hardware efficiency is a crucial requirement, should these erasure qubits be used in quantum processors or error-correcting codes.

Here we present a dual-rail encoding within a single fixed-frequency superconducting multimode transmon qubit. The three island, two junction device comprises two strongly coupled transmonlike modes with a detuning of 1.5 GHz. We perform all-microwave control of the logical states using a single capacitively coupled coaxial control line. A resonator on the opposing side of the substrate allows for the dispersive readout of the multimode state of the device, with an error-detected logical state assignment fidelity of above 99%. In addition, we are able to perform a weak error-detection measurement using the same resonator with minimal dephasing of the logical state, enabling mid-circuit error detection operations. Finally, we report logical coherence metrics, and discuss its relationship to noise and decoherence in transmon qubits.