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While many codes have been studied in the context of the abstract model of depolarizing noise arising from the action of random Pauli operators on the qubit, the realistic error model for a given qubit platform is often more complex, which presents both opportunities and challenges.

For example, qubits encoded in cat-codes in superconducting resonators can have strongly biased noise 11, leading to significantly higher thresholds 12, 13 given suitable bias-preserving gate operations for fault-tolerant syndrome extraction 14. The realization of biased noise models and bias-preserving gates for Rydberg atom arrays has also been discussed 15.

On the other hand, many qubits also exhibit some level of leakage outside of the computational space 6, 16, which requires extra gates in the form of leakage-reducing units, decreasing the threshold 17.Īnother type of error is an erasure, or detectable leakage, which denotes an error at a known location. For example, a four-qubit quantum code is sufficient to correct a single erasure error 19, and the surface code threshold under the erasure channel approaches 50% (with perfect syndrome measurements), saturating the bound imposed by the no-cloning theorem 20.Įrasures are significantly easier to correct than depolarizing errors in both classical 18 and quantum 3, 19 settings.

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