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Cheatsheets for things I use or do


Surface Code

Logical Operators

In this picture, given that, the blue patches are $Z$ stabilizers and the $X$ stabilizers are yellow, the logical operator $Z$ ($X$) is represented by a horizontal (vertical) series of $Z$s ($X$s) applied to data qubits (the white ones, the grey ones are syndrome qubits for parity measurements).

For example, given a numbering starting from (1, 1) in the top left, and going down to the bottom right at (5, 5) for the data qubits, a possible logical Z (typically notated $\tilde{Z}$) could be $Z$s applied to $(3, 1), (3, 2), \ldots (3, 5)$, aka the row in the middle. Notice, then, that the ends touch the $Z$ weight-two stabilizers, which means that the logical operators commute with all stabilizers (makes sense)!

This idea can be extended to the $\tilde{X}$ as well.

Patch-based Surface Code Shenanigans

Patch-based SC uses lattice surgery!

TBD.

Vim

  • You can do Ctrl+k and then two characters to get digraphs in Vim; use :digraphs to check what the codes are for specific symbols!