分子光镊阵列的表面码量子纠错：编码、布局与关联噪声
Surface-Code Quantum Error Correction for Molecular Tweezer Arrays: Encoding, Layout, and Correlated Noise
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中文总结 AI 辅助
本文针对分子光镊阵列的表面码量子纠错，构建了编码映射，对比不同旋转量子位维度的编码，揭示关联损耗空间嵌入的重要性及单扇区基准的局限性。
中文摘要 AI 辅助
被束缚在光镊阵列中的极性分子为量子信息处理提供了极具前景的平台，其具备精准操控能力与长程相互作用，可实现高保真度的门操作。我们研究该系统中的量子纠错，并分析底层物理噪声的影响。我们构建了从分子光镊阵列到旋转表面码的映射，其中阵列的一项具体规格——即哪些码量子比特共享一个分子、以及这些分子的位置——同时决定了关联擦除结构与偶极交换图。我们在宣告式分子损耗、相干偶极交换与不完善宣告的条件下，对比了旋转量子位维度（D）为2和4的分子编码。研究发现，D=4编码采用空间分散配对时，其有限距离交叉出现在与D=2大致相同的每分子损耗率下，但所需分子数量减少48%-49%，代价是亚阈值逻辑错误增加6%-10%。固定编码仅改变空间嵌入会产生显著更大的影响：沿晶格方向配对两个共位量子比特，会产生约50倍的逻辑扇区不对称性。在模拟距离（d=5、7、9）下，不利扇区的逻辑错误随码距增加几乎无抑制，而有利扇区的逻辑错误则提升1.5-2.3倍。我们还发现，交换相互作用的Pauli扭转会高估逻辑错误率，这可归因于该相互作用的激发守恒结构。这些结果表明，关联损耗单元的空间嵌入是分子架构的重要设计参数，且当关联损耗具有方向结构时，单扇区基准可能不足。
英文摘要
Polar molecules trapped in optical tweezer arrays offer a promising platform for quantum information processing, providing precise control and long-range interactions that enable high-fidelity gate operations. We investigate quantum error correction in this system and show the influence of underlying physical noise. A mapping is constructed from a molecular tweezer array onto a rotated surface code in which a single specification of the array, namely, which code qubits share a molecule and where those molecules are located, determines both the correlated erasure structure and the dipolar exchange graph. We compare molecular encodings with rotational qudit dimensions (D), two and four under heralded molecular loss, coherent dipolar exchange, and imperfect heralding. It is found that a D= 4 encoding with spatially dispersed pairing exhibits a finite distance crossing at approximately the same per molecule loss rate as D= 2, while using 48-49 % fewer molecules, at the cost of a 6-10 % increase in sub-threshold logical error. Fixing the encoding and varying only the spatial embedding produces substantially larger effects: pairing the two co-located qubits along a lattice direction yields a logical-sector asymmetry of approximately fifty times. Over the simulated distances (d = 5, 7, 9), the disfavoured sector shows little or no suppression of logical error with increasing code distance, whereas the favoured sector improves by a factor of 1.5-2.3. We also find that Pauli twirl of the exchange interaction overestimates the logical error rate, which we attribute to the excitation-conserving structure of the interaction. These results reveal that the spatial embedding of correlated loss units is an important design parameter for molecular architectures and that single-sector benchmarks may be insufficient when correlated loss has directional structure.
