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Understanding PEPS Tensor Network for Surface Code

$i$ represents the qubit before stabilizing (before act with $W$ / the input to $W$) and $i'$ is the output (after $W$). We can think of e.g. $XXXX$ stabilizer as creating a superposition of 2 cases: ...
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Lattice surgery: how is merged code stabilized by 'merging stabilizers' if their measurement outcome can be -1?

As far as computation goes, it doesn't matter whether the state stabilized by a stabilizer or its negation. What matters is that you know the sign of the stabilizer with confidence, via the ...
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