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It is proved that the optimal $\mathrm{T}$ count is $\Theta\left(n+\min\left\{s, m+\log(2^{n+1}/s)}\right\}\right)$.
A scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations is introduced, suppressing the residual logical errors that limit existing partially fault-tolerant approaches.
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