Abstract: We employed the techniques from [Phys. Rev. A \textbf70, 052328 (2004)/arXiv:0406196] to analytically study two set of quantum circuits containing one T gate/magic ∣T⟩=2∣0⟩+i∣1⟩ state. These include the T state via gate teleportation and magic state injection on the rotated surface code.
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