  The overhead of quantum error correction (QEC) poses a major bottleneck for
realizing fault-tolerant computation. To reduce this overhead, we exploit the
idea of erasure qubits, relying on an efficient conversion of the dominant
noise into erasures at known locations. We start by introducing a formalism for
QEC schemes with erasure qubits and express the corresponding decoding problem
as a matching problem. Then, we propose and optimize QEC schemes based on
erasure qubits and the recently-introduced Floquet codes. Our schemes are
well-suited for superconducting circuits, being compatible with planar layouts.
We numerically estimate the memory thresholds for the circuit noise model that
includes spreading (via entangling operations) and imperfect detection of
erasures. Our results demonstrate that, despite being slightly more complex,
QEC schemes based on erasure qubits can significantly outperform standard
approaches.

Quantum Physics