quantum circuit applying entangling gates to several qubits simultaneously. Unwanted Z-Z coupling on superconducting cross-resonance CNOT gates, is a commonly occurring unitary crosstalk noise that severely limits the state fidelity. This work presents (1) method of tracing unitary errors, which exploits their sensitivity to the arrangement of CNOT gates in the circuit and (2) correction scheme that modifies original circuit by inserting carefully chosen compensating gates (single- or two-qubit) to possibly undo unitary errors. On two vastly different types of IBMQ processors offering quantum volume 8 and 32, our experimental results show up to 25% reduction in the infidelity of [[7, 1, 3]] code |+> state. Our experiments aggressively deploy forced commutation of CNOT gates to obtain low noise state-preparation circuits. Encoded state initialized with fewer unitary errors marks an important step towards successful demonstration of fault-tolerant quantum computers.