I study computer science and wanted to get into the field of quantum computing. Right now, I'm trying to tackle the subject of quantum error correcting codes. As is the usual, I've started with Shor's code: Given a qubit, we transform it to a product of 9 qubits:
We measure the syndromes of every qubit to find out if an error occurred, and if it did we use the corresponding operator to fix it.
Now, I'm reading up on the Toric code as proposed by Kitaev. I don't completely understand how it works: I know it can protect two qubits, so lets assume we've got: $|a>, |b>$
I don't understand how will their lattice look like - how can we "write down" the lattice using standard notation (like how we wrote Shor's 9 qubit representation)?