# Q-Pandora Unboxed: Characterizing Resilience of Quantum Error Correction Codes Under Biased Noise
## 3 Related Works  
In a seminal work by [PERSON] and [PERSON], they investigated the experimental implementation of a distance-3 surface code under realistic quantum noise conditions [26]. Their simulations, which were conducted under amplitude and phase damping, suggested that the Pauli-twirl approximation tends to give a pessimistic threshold estimate. While their research provided valuable insights into this specific type of surface code, it lacked a broader exploration of the noise resilience of various QECCs. [PERSON] and [PERSON] took a methodologically distinct approach by proposing a tensor network algorithm for simulating the surface code under arbitrary local noise [27]. Their work stood out because it addressed the challenges of simulating the surface code under realistic conditions, whereas many previous studies had relied on overly simplified noise models. Despite the novelty of their method, their research was exclusively centered on the surface code, not extending its scope to other QECCs. [PERSON] et al. made significant contributions by addressing biased noise challenges in quantum computing [28]. They introduced a high-threshold decoder tailored specifically for a noise-tailored surface code. Their innovative approach, built upon minimum-weight perfect matching, was tailored to exploit symmetries in biased noise scenarios. While this approach achieved fault-tolerant thresholds exceeding 6%, their research was primarily aimed at biased noise scenarios, without a broader examination of other noise conditions. In a later work, [PERSON] et al. delved deeper into tailoring surface codes for scenarios dominated by highly biased noise, especially dephasing [29]. Their results revealed that with certain modifications, the surface code can achieve exceptionally high error-correction thresholds. Moreover, they provided evidence that the threshold error rate of the surface code closely aligns with the hashing bound across all biases. However, their focus remained on highly biased noise scenarios, not extending to a wider range of noise conditions. The practical challenges of achieving low error rates in quantum computing were brought to the forefront by Google Quantum AI [30]. Their work emphasized that while QECCs can indeed help in reducing error rates by encoding logical qubits within multiple physical qubits, this increase in physical qubits can also be a source of more errors. Nonetheless, using a superconducting qubit system and a distance-5 surface code logical qubit, they demonstrated the potential to overcome these additional error sources. [PERSON] et al. focused on the realization of repeated quantum error correction by leveraging a distance-3 surface code in a superconducting system with 17 physical qubits [17]. Their work aligned with ours in employing the STIM simulator, which further attested to its efficacy in producing results that closely mirror those from actual quantum computers. Another noteworthy direction in quantum error correction is Microsoft's approach leveraging topological quantum computing with Majorana zero modes [38; 39; 40]. Instead of relying solely on software-level error correction such as surface codes, their strategy aims to build topological qubits that are intrinsically resilient to local noise due to the non-local encoding of quantum information. This hardware-level fault tolerance, if realized, could significantly reduce the overhead associated with traditional QECCs. However, despite its theoretical promise, this approach is still in the experimental stage, and the practical realization of stable Majorana-based qubits remains a significant challenge. Nonetheless, it represents a compelling complement to surface-code-based architectures and highlights the diversity of strategies being pursued in fault-tolerant quantum computing. In comparison to the aforementioned studies, our research offers a comprehensive perspective on QECCs. We delve deeper into the resilience of surface codes, expanding the analysis to a diverse range of noise models and error types.