  Quantum error correction codes (QECCs) are critical for realizing reliable
quantum computing by protecting fragile quantum states against noise and
errors. However, limited research has analyzed the noise resilience of QECCs to
help select optimal codes. This paper conducts a comprehensive study analyzing
two QECCs - rotated and unrotated surface codes - under different error types
and noise models using simulations. Among them, rotated surface codes perform
best with higher thresholds attributed to simplicity and lower qubit overhead.
The noise threshold, or the point at which QECCs become ineffective, surpasses
the error rate found in contemporary quantum processors. When confronting
quantum hardware where a specific error or noise model is dominant, a
discernible hierarchy emerges for surface code implementation in terms of
resource demand. This ordering is consistently observed across unrotated, and
rotated surface codes. Our noise model analysis ranks the code-capacity model
as the most pessimistic and circuit-level model as the most realistic. The
study maps error thresholds, revealing surface code's advantage over modern
quantum processors. It also shows higher code distances and rounds consistently
improve performance. However, excessive distances needlessly increase qubit
overhead. By matching target logical error rates and feasible number of qubits
to optimal surface code parameters, our study demonstrates the necessity of
tailoring these codes to balance reliability and qubit resources. Conclusively,
we underscore the significance of addressing the notable challenges associated
with surface code overheads and qubit improvements.
