# Q-Pandora Unboxed: Characterizing Resilience of Quantum Error Correction Codes Under Biased Noise
## 6 Strategies for Optimal and Scalable Code Selection
### Assessing Surface Codes Relative to Current State-of-the-Art Quantum Processors  
While minimizing the logical error rate, we must also consider qubit overhead, which varies with error types and noise models. As exemplified in Figure 9a, if we are dealing with a quantum hardware system predominantly affected by depolarizing errors, along with a physical noise of \(0.5\times 10^{-2}\) (higher than the current state-of-the-art error rates) and a target logical error rate of \(10^{-23}\), we will need approximately 1000 qubits. Reducing the logical error rate further may be infeasible due to qubit cost and scarcity. Thus, identifying the right surface code parameters can help balance between the logical error rate and qubit overhead. Table 3 illustrates the interplay between code parameters (distance and rounds), overhead (qubit and gate counts), and system improvement for a surface code in the most realistic scenario: a circuit-level noise model with a physical error rate of \(10^{-3}\). It is apparent that the system's performance significantly improves, up to \(10^{12}\) times, with an increase in resources, reaching this point with a distance-25 rotated surface code employing 580 qubits and 2040 gates. Continuous resource augmentation can indeed boost error rate improvement in quantum error correction codes. However, constraints, whether they be technological or logistical, impose a ceiling on resource availability.  
Figure 8: Logical error rate vs. code distance for rotated surface codes at a physical noise level of \(0.5\times 10^{-2}\) for (**a**) various error types and (**b**) noise models. The experiments are projected to distance 30 with \(rounds=distance\times 3\). The results confirm that the optimal surface code is not always needed. By understanding the target logical error rate for certain noise types or models, we can identify appropriate surface code parameters, reducing unnecessary gate and qubit overhead.  
Figure 9: Logical error rate vs. number of qubits for rotated surface codes at a physical noise level of \(0.5\times 10^{-2}\) for (**a**) various error types and (**b**) noise models. The experiments are projected to 1000 qubits. The findings reveal that the proper determination of surface code parameters can effectively balance the logical error rate and qubit overhead.  
While it is natural to strive for the most efficient surface code utilization in every situation, this might not always be necessary or even feasible. It is crucial to consider the specific requirements and constraints of each scenario. By understanding the target logical error rate and the available resources in terms of qubit overhead, we can tailor our approach to the specific type of noise or noise model present. This way, we can determine the parameters of a rotated surface code that are best suited for the situation at hand.  
Our analysis of QEC codes highlights that while surface codes effectively safeguard quantum data, they come with significant overhead. For instance, a distance-5 rotated surface code needs about 60 qubits, a challenge given the limited qubits in today's quantum computers. Moreover, the current hardware struggles with the precision needed for two-qubit gates. Despite these challenges, the promising error tolerance thresholds suggest surface codes are attainable. The focus should be on increasing both the number and quality of qubits. Enhancing qubit stability and gate fidelity will push error rates below critical thresholds. Optimizing decoding methods and crafting efficient codes will further bridge the gap between existing hardware and QEC demands, paving the way for reliable quantum computing.