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I've heard people mention that one can teleport a gate from one QEC code into another, but I am trying to better understand operationally what exactly this entails, and whether there are any restrictions on the two codes used. More specifically, I'd be interesting in seeing the set of operations needed to:

  1. Teleport a magic state from say, a 7x7 surface code into a 11x11 surface code, to implement a T gate in the latter, or
  2. Do the same but from a surface code into a color code. Thanks a lot!
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This paper was published a few days ago which shows how to convert magic states encoded in the color code to magic states in the surface code. You asked about the reverse transformation (surface to color), but the general approach could be helpful.

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