Toward Fault-Tolerant Variational Optimization: QAOA under [[4,2,2]] Error Detection

We present a partially fault-tolerant implementation of QAOA based on the $[[4,2,2]]$ error-detection code, targeting the Max-Cut problem on a square graph. Our main contribution is a novel ancilla-mediated logical $R_{ZZ}$ gate enabling interactions between qubits in different $[[4,2,2]]$ blocks. W