发表机构
IIT Madras; Center for Quantum Information, Communication and Computing, IIT Madras（印度理工学院马德拉斯分校; 印度理工学院马德拉斯分校量子信息、通信与计算中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对广义振幅阻尼噪声，提出概率近似量子纠错框架，构造五量子比特置换不变码，使保真度损失平方级降低，优于现有QEC码。
AI 中文摘要
量子纠错（QEC）在保护量子信息免受退相干影响以及实现可扩展、可靠的量子计算中发挥着至关重要的作用。如今影响量子硬件的最现实且普遍存在的噪声源之一是广义振幅阻尼（GAD）噪声。传统的确定性QEC码由于其固有结构，难以纠正GAD噪声，导致保真度损失随阻尼强度线性增长。在本工作中，我们引入了概率近似量子纠错（PAQEC）框架，该框架结合了近似QEC的灵活性与后选择恢复的潜力，实现了高保真度、资源高效的纠错。我们构造了一个五量子比特置换不变码，在概率恢复下，其保真度损失与阻尼强度的平方成正比，从而优于现有QEC码。将PAQEC表述为优化问题，我们提出了一种基于Charnes-Cooper和半定规划的数值技术，以识别任何PAQEC码的最优恢复映射。我们的结果确立了PAQEC作为开发针对现实噪声定制的资源高效、高保真量子码的强大工具，对近期量子设备和未来容错架构具有广阔前景。
英文摘要
Quantum error correcting (QEC) plays a crucial role in protecting quantum information against decoherence and enabling scalable, reliable quantum computing. One of the most realistic and ubiquitous sources of noise affecting quantum hardware today is generalized amplitude-damping (GAD) noise. Conventional, deterministic QEC codes struggle to correct for GAD noise because of their inherent structure, leading to fidelity losses that scale linearly with the damping strength. In this work, we introduce the framework of probabilistic approximate quantum error correction (PAQEC), that combines the flexibility of approximate QEC with the potential of post-selected recovery, enabling high-fidelity, resource-efficient error correction. We construct a five-qubit permutation-invariant code that, under probabilistic recovery, achieves a fidelity loss quadratic in the damping strength, thus outperforming existing QEC codes. Formulating PAQEC as an optimization problem, we present a numerical technique based on Charnes-Cooper and semidefinite programming to identify the optimal recovery map for any PAQEC code. Our results establish PAQEC as a powerful tool for developing resource-efficient, high-fidelity quantum codes tailored to realistic noise, with promising implications for near-term quantum devices and future fault-tolerant architectures.
Comments15+3 pages, 5+1 figures
