Leakage Detection in Integer Fluxonium Qubits

Leakage errors are damaging to the fidelity of quantum operations. Detecting and converting leaked qubits back to computational subspace is called erasure conversion. Erasure conversion makes the location of error available and error correction decoding easier. Erasure conversion has been proposed for superconducting circuits [1-2] and ¹⁷¹Yb atoms [3-4]. Recently erasure conversion of ¹⁷¹Yb has been experimentally demonstrated [5]. We propose a protocol of erasure conversion on integer fluxonium qubits. We analyze the physical process of erasure detection to find settings with high detection success rate and minimal effect on the computational subspace. The converted erasure in our protocol has a biased Pauli noise profile, and the computational subspace has long coherence times because of the low-frequency nature of the computational subspace. 

[1] Teoh et al., PNAS 120 (41) e2221736120 (2023).

[2] Kubica et al., arXiv:2208.05461 [quant-ph] (2022).

[3] Wu et al., Nat Commun 13, 4657 (2022).

[4] Sahay et al., arXiv:2302.03063 (2023).

[5] Ma et al., arXiv:2305.05493 (2023).