A superconducting dual-rail cavity qubit with erasure-detected logical measurements

A critical challenge in developing scalable quantum systems is correcting the accumulation of errors while performing operations and measurements. It is known that systems where dominant errors can be detected and converted into erasures have relaxed requirements for quantum error correction. Recently, it has been proposed that this can be achieved using a dual-rail encoding of quantum information in the microwave photon states of two superconducting cavities. One necessary step to realize this erasure qubit is to demonstrate a measurement and to flag errors as erasures. In this work, we demonstrate a projective logical measurement of a dual-rail cavity qubit with integrated erasure detection and measure the qubit idling errors. We measure the logical state preparation and measurement errors at the 0.01% level and detect over 99% of the cavity decay events as erasures. We use the precision of this measurement protocol to distinguish different types of error in this system, finding that although decay errors occur with a probability of approximately 0.2% per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 150 times less frequently. These findings represent a confirmation of the expected error hierarchy necessary to concatenate dual-rail cavity qubits into a highly efficient erasure code.