Figure 2
From: Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
(a) Kitaev toric code. Each link is associated with a code qubit. The code is realized in the L × L square sheet on the torus, hence there are 2L2 code qubits. Stabilizer generators of X-type are represented by stars (tensor product of X's acting on four qubits building a particular star) and of Z-type by plaquettes (tensor product of Z's acting on four qubits which merge to a particular plaquette). Due to periodic boundary conditions there are 2(L2 − 1) independent stabilizer generators. Thus, one is able to encode 2 qubits. Exemplary logical operators associated with those qubits are marked in a picture in such a way that XL,i and ZL,i anticommute, where i = 1, 2. (b) Preparation of a lattice. Qubits to be encoded are marked by red dots. Qubits in green and blue regions are initialised in states |0〉 and |+〉, respectively.
