Noisy intermediate-scale quantum algorithms, which run on noisy quantum computers, should be carefully designed to boost the output state fidelity. While several compilation approaches have been proposed to minimize circuit errors, they often omit the detailed circuit structure information that does not affect the circuit depth or the gate count. In the presence of spatial variation in the error rate of the quantum gates, adjusting the circuit structure can play a major role in mitigating errors. In this article, we exploit the freedom of gate reordering based on the commutation rules to show the impact of gate error propagation paths on the output state fidelity of the quantum circuit, propose advanced predictive techniques to project the success rate of the circuit, and develop a new compilation phase postquantum circuit mapping to improve its reliability. Our proposed approaches have been validated using a variety of quantum circuits with different success metrics, which are executed on IBM quantum computers. Our results show that rescheduling quantum gates based on their error propagation paths can significantly improve the fidelity of the quantum circuit in the presence of variable gate error rates.