# Circuit for fault tolerant syndrome measurements Steane Code

I was exploring this paper: https://arxiv.org/pdf/1505.07390.pdf The paper describes the syndrome measurement for the [7,1,3] code. I was looking a fault-tolerant syndrome measurement and found this Figure. I was wondering what is $$\psi_{L}$$ and what is its function to the circuit, and I am thinking if I can remove $$\psi_{L}$$ and apply CNOT gate from $$|0\rangle _{L}$$ to $$|+\rangle_{L}$$ directly? Will it change the property of the circuit especially the fault-tolerant property.

It will be great to share the similar kind of circuit for [7,1,3] steane code for QEC.

The circuit in the diagram is for fault-tolerantly measuring the error syndrome of the logical qubit $$|\psi_L\rangle$$. I.e., $$|\psi_L\rangle$$ is the logical qubit (a qubit encoded into 7 qubits using the Steane code) whose errors you want to correct. So removing it wouldn't make sense.