发表机构
Freie Universität Berlin; Technology Innovation Institute (TII); Tsinghua University; Helmholtz-Zentrum Berlin für Materialien und Energie（柏林自由大学; 技术创新研究所; 清华大学; 亥姆霍兹柏林材料能源中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明费米子量子纠错必然需要非高斯操作，且所需非高斯门数量随码距和模式数线性增长，揭示了其内在资源开销及与玻色子系统的本质区别。
AI 中文摘要
费米子平台为量子计算提供了引人注目的架构，从基于拓扑保护的马约拉纳量子比特到费米子冷原子。然而，要实现可扩展性，它们需要量子纠错。在这项工作中，我们证明了任何精确且足够近似的费米子量子纠错必然需要非高斯操作，超越二次动力学中的自由费米子区域。这与量子比特设置形成鲜明对比，在量子比特设置中，可高效经典模拟的稳定子操作构成了量子纠错的标准框架。具体而言，我们展示了任何非平凡的费米子纠错码的逻辑空间不包含纯费米子高斯态，利用了费米子纠错与维克定理之间的根本不相容性。我们进一步表明，用于酉码字制备所需的有界权重非高斯门数量随码距和编码模式数量至少线性增长，揭示了内在的资源开销，该开销随错误保护强度和逻辑容量同时增加。此外，我们分析了费米子高斯操作在纠缠蒸馏中的性能，揭示了它们与玻色子对应物的区别。我们的结果从物理实现和经典模拟的角度揭示了费米子纠错的基本困难，暗示了与费米子物质相和态制备复杂性的联系。
英文摘要
Fermionic platforms offer compelling architectures for quantum computing, ranging from topologically protected Majorana-based qubits to fermionic cold atoms. To achieve scalability, however, they require quantum error correction. In this work, we prove that any exact and sufficiently accurate approximate fermionic quantum error correction necessarily requires non-Gaussian operations, beyond the free-fermion regime of quadratic dynamics. This is in sharp contrast to the qubit setting, where the efficiently classically simulable stabilizer operations form the standard framework for quantum error correction. Specifically, we show that the logical space of any non-trivial fermionic error-correcting code contains no pure fermionic Gaussian state, utilizing a fundamental incompatibility between fermionic error correction and Wick's theorem. We further show that the required number of bounded-weight non-Gaussian gates for unitary codeword preparation grows at least linearly with both the code distance and the number of encoded modes, revealing an intrinsic resource overhead that increases simultaneously with error-protection strength and logical capacity. Furthermore, we analyze the performance of fermionic Gaussian operations in entanglement distillation, revealing a distinction from their bosonic counterparts. Our results reveal fundamental difficulties for fermionic error correction from the perspectives of both physical implementation and classical simulation, suggesting connections to fermionic phases of matter and state preparation complexity.
Comments7+28 pages, comments are very welcome!
