Characterization and mitigation of leakage-conditional errors for quantum error correction based on superconducting transmon qubits

Leakage outside the computational subspace of superconducting transmon qubits is a threatening error for quantum error correction (QEC). Transmons can remain leaked for many QEC rounds, during which they can propagate correlated errors on the neighboring qubits [1, 2], significantly impacting the code performance. This has motivated the use of leakage-reduction units (LRUs), which limit the leakage lifetime to a single round [1, 2, 3], thereby reducing the impact of leakage. However, leakage can still occur in each round, and any subsequent two-qubit gate involving a leaked transmon can spread further errors. These gates can also excite leaked transmons to even higher-excited states, which the LRUs might not be designed to handle. We characterize the leakage-conditional errors induced by controlled-phase gates between flux-tunable transmons and explore approaches to mitigate these errors.



[1] M. McEwen et al., Nat Comm. 12, 1761 (2021)

[2] K. C. Miao et al., Nat. Phys. 19, 1780–1786 (2023)

[3] N. Lacroix et al., arXiv 2309.07060 (2023)