The benefits and costs of quantum error correction with erasure qubits

The overhead of quantum error correction (QEC) poses a major bottleneck for realizing fault-tolerant computation. To reduce this overhead, we exploit the recently introduced idea of erasure qubits, relying on an efficient conversion of the dominant noise into erasures at known locations. Whereas previous works have considered overly simplistic models of erasure qubits, we provide for the first time a comprehensive assessment of the benefits and costs of erasure qubits, taking into account imperfect erasure detection and reset that introduce additional noise, and spreading of erasures. To do this, we introduce a general formalism for QEC schemes with erasure qubits and prove a reduction of the corresponding decoding problem to decoding stabilizer circuits. In addition to our novel approximate decoding methods, this allows us to numerically simulate memory thresholds and estimate the overhead of QEC with erasure qubits. We also consider optimizations in the QEC code design, the syndrome extraction circuit, and the hardware implementation of the erasure qubit. Our results indicate that QEC schemes based on erasure qubits can significantly outperform standard approaches.