Q-Pandora Unboxed: Characterizing Resilience of Quantum Error Correction Codes Under Biased Noise

Quantum error correction codes (QECCs) are essential for reliable quantum computing as they protect quantum states against noise and errors. Limited research has explored the resilience of QECCs to biased noise, critical for selecting optimal codes. We examine how different noise types impact QECCs, considering the varying susceptibility of quantum systems to specific errors. Our goal is to identify opportunities to minimize the resources—or overhead—needed for effective error correction. We conduct a detailed study on two QECCs—rotated and unrotated surface codes—under various noise models using simulations. Rotated surface codes generally perform better due to their simplicity and lower qubit overhead. They exceed the noise threshold of current quantum processors, making them more effective at lower error rates. This study highlights a hierarchy in surface code implementation based on resource demand, consistently observed across both code types. Our analysis ranks the code-capacity model as the most pessimistic and the circuit-level model as the most realistic, mapping error thresholds that show surface code advantages. Additionally, higher code distances improve performance without excessively increasing qubit overhead. Tailoring surface codes to align with the target logical error rate and the biased physical error profile is crucial for optimizing reliability and resource use.