Circuit for implementing Steane's code for Quantum Error Correction

One way of defining the Steane code is via its stabilizers. There's a set of operators ${K_n}_{n=1}^6$ which all commute, such that a state in the code space is defined by being the $+1$ eigenstate of all these operators.

So, you can perform syndrome extraction simply by measuring the value of each stabilizer. This is a standard circuit, (the $sigma_1otimesldotsotimessigma_n$ corresponds to a single $K_i$ term in this setting).

One very simple way that you can produce a codeword in the code space is simply to start with $|psirangle$ as any state you want. Perform syndrome extraction and error correction on it, and the result must be a word in the space.

In fact, if you set $|psirangle=|0000000rangle$, you'll get the logical 0 state because this is a $+1$ eigenstate of $Z^{otimes 7}$. Moreover, this state is already the $+1$ eigenstate of all the $Z$-type stabilizers so you don't have to measure any of those.

There do exist unitary encoding methods, but from the conceptual point of view, this is a very simple method that generalises to any stabilizer code.