标题： 容错校正编码的[[7,1,3]] Steane码在二维网格上的实现 显示英文标题

标题： Fault-tolerant correction-ready encoding of the [[7,1,3]] Steane code on a 2D grid

摘要： 实用的量子计算严重依赖于能够以容错的方式执行量子纠错的能力。 容错编码是一个关键的第一步，仔细考虑随后的纠错循环对于确保编码的有效性和兼容性至关重要。 在这项工作中，我们研究了多种准备好纠错的编码方法，以在二维网格上容错地准备[[7,1,3]] Steane码的零逻辑态。 通过数值模拟，我们证明了带有少量标志桥（Flag-Bridge）量子比特的奇偶校验编码比基于验证的编码表现更好，因为它能实现更低的错误率，并允许灵活调整性能-效率之间的权衡。 此外，奇偶校验方法可以启用一种紧凑的混合协议，该协议结合了编码和纠错功能，能够匹配单独纠错协议的性能，前提是编码完美无误。 令人惊讶的是，与资源密集型的Steane纠错相比，在嘈杂环境中这种方法仍然具有实际优势。 这些发现突显了使用标志桥量子比特的方法作为嘈杂近期量子硬件的一种强大且可适应的解决方案。 显示英文摘要

摘要： Practical quantum computation heavily relies on the ability to perform quantum error correction in a fault-tolerant manner. Fault-tolerant encoding is a critical first step, and careful consideration of the error correction cycle that follows is essential for ensuring the encoding's effectiveness and compatibility. In this work, we investigate various correction-ready encoding methods to fault-tolerantly prepare the zero-logical state of the [[7,1,3]] Steane code on a 2D grid. Through numerical simulations, we demonstrate that parity-check encoding with a few Flag-Bridge qubits outperforms verification-based encoding by achieving lower error rates and allowing flexible tuning of the performance-efficiency trade-off. Additionally, parity-check approach enables a compact hybrid protocol that combines encoding and error correction, capable of matching the performance of a standalone error correction protocol with perfect encoding. Surprisingly, compared to the resource-intensive Steane error correction, this low-overhead method still offers a practical advantage in noisy settings. These findings highlight the approach with Flag-Bridge qubits as a robust and adaptable solution for noisy near-term quantum hardware.