AI 中文总结
该研究证明了非Clifford容错的限制，排除了超越SQL的量子计量学，发现恒定强度信号对齐噪声会阻碍量子计量学超越SQL的渐近优势。
AI 中文摘要
量子计量学有望实现超越标准量子极限（SQL）的二次加速，但在实际场景中，信号对齐噪声预计会阻碍这一优势。绕过已知禁果定理的一个潜在途径是将传感器编码在量子码中，其中物理信号作为逻辑门横向作用。因此，理解横向非Clifford门的限制对量子计量学和容错量子计算都至关重要。本文中，我们证明了此类限制并将其应用于横向传感。对于任意支持Clifford层级D级横向逻辑作用的距离d≥3的稳定子码，每个稳定子生成集必须包含权重至少为2^D的校验。此外，任意r级级联实现满足r≤⌊log₂n/D⌋，当应用于超越SQL的计量学时，这迫使r=1并排除级联。我们进一步表明，若n量子比特码的校验包含权重为Ω(1/(n|θ|²))的不可约稳定子，则小角度θ的横向单量子比特旋转仅能诱导非平凡逻辑作用。在此权重以下，许多单量子比特错误与每个稳定子或逻辑泡利算子对易，仅被高权重校验检测，因此其症候群无法通过低权重正规子测量容错重构。由于超越SQL的横向传感要求|θ|=o(n⁻¹/²)，症候群提取所需的校验权重随n发散。最后，我们证明了更广泛的计量学禁果定理，避免了量子Cramér-Rao界的假设：即使使用有偏估计器、非稳定子或近似编码、量子存储器、中间测量或自适应控制，恒定强度的信号对齐噪声也会排除交流或直流传感中超越SQL的任何渐近优势。
英文摘要
Quantum metrology promises a quadratic speedup over the standard quantum limit (SQL), but signal-aligned noise is expected to preclude this advantage in realistic settings. A potential route around known no-go results is to encode the sensors in a quantum code where the physical signal acts transversally as a logical gate. Understanding restrictions on transversal non-Clifford gates is therefore central to both quantum metrology and fault-tolerant quantum computation. Here, we prove such restrictions and apply them to transversal sensing. For any stabilizer code of distance $d\ge 3$ supporting a transversal logical action in level $D$ of the Clifford hierarchy, every stabilizer generating set must contain a check of weight at least $2^D$. Moreover, any $r$-level concatenated realization satisfies $r\leq \lfloor \log_2 n/D\rfloor$, forcing $r=1$ and ruling out concatenation when applied to beyond-SQL metrology. We then show that transversal single-qubit rotations by a small angle $θ$ can only induce a nontrivial logical action on an $n$-qubit code if its checks include irreducible stabilizers of weight $Ω(1/(n|θ|^2))$. Here, many single-qubit errors commute with every stabilizer or logical Pauli below this weight and are only detected by a high-weight check, so their syndromes cannot be fault-tolerantly reconstructed from low-weight normalizer measurements. Since beyond-SQL transversal sensing requires $|θ| = o(n^{-1/2})$, the weight of checks required for syndrome extraction diverges with $n$. Finally, we prove a broader metrological no-go theorem that avoids the assumptions of the quantum Cramér-Rao bound: constant-strength signal-aligned noise rules out any asymptotic advantage over the SQL in AC or DC sensing, even with biased estimators, nonstabilizer or approximate encodings, quantum memory, intermediate measurements, or adaptive control.
Comments6+20 pages, 1 figure
