The boundaries and topological defects of the color code*

We give a thorough exploration of the color code phase to find all of its boundaries and domain walls.
This gives us a new playground to discover new quantum error correcting codes and ways of performing gates.
Our exploration uncovered improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits.