Demonstrating a superconducting dual-rail cavity qubit with erasure-detected logical measurements

A critical challenge in developing scalable error-corrected quantum systems is the accumulation of errors while performing operations and measurements. One promising approach is to design a system where errors can be detected and converted into erasures. A recent proposal aims to do this using a dual-rail encoding with superconducting cavities. In this work, we implement such a dual-rail cavity qubit and use it to demonstrate a projective logical measurement with erasure detection. We measure logical state preparation and measurement errors at the $0.01\%$-level and detect over $99\%$ of cavity decay events as erasures. We use the precision of this new measurement protocol to distinguish different types of errors in this system, finding that while decay errors occur with probability $\sim 0.2\%$ per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 170 times less frequently. These findings represent the first confirmation of the expected error hierarchy necessary to concatenate dual-rail erasure qubits into a highly efficient erasure code.