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Stabilized cat codes can provide a biased noise channel with a set of bias-preserving (BP) gates, which can significantly reduce the resource overhead for fault-tolerant quantum computing.
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Despite the energy gap Δ 1 < 0 \Delta_{1}<0 is negative in the rotating frame, the excitation energy ω 0 + Δ 1 > 0 \omega_{0}+\Delta_{1}>0 is still positive in the lab frame, with oscillator frequency ω 0 \omega_{0}
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