Optimizing Quantum Error-Correction Protocols with Erasure Qubits

Erasure qubits offer a promising avenue toward reducing the overhead of quantum error correction (QEC) protocols. However, they require additional operations, such as erasure checks, that may add extra noise and increase the run-time of QEC protocols. To assess the benefits provided by erasure qubits, we focus on the performance of the surface code as a quantum memory. In particular, we analyze various erasure check schedules, find the correctable regions in the phase space of error parameters, and probe the subthreshold scaling of the logical error rate. We then consider a realization of erasure qubits in the superconducting hardware architectures via dual-rail qubits. We use the standard transmon-based implementation of the surface code as the performance benchmark. Our results indicate that QEC protocols with erasure qubits can outperform the ones with state-of-the-art transmons, even in the absence of precise information about the locations of erasure errors.