发表机构
Peking University; Freie Universität Berlin（北京大学; 柏林自由大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出距离放大器模块化构造，通过张量积放大qLDPC码的码距与认证电路距离，并证明乘法关系，实现超高距离量子存储器的可扩展构建。
AI 中文摘要
大的码距本身并不能保证量子存储器得到良好保护，因为在综合征提取过程中的故障可能传播为相关的数据错误。随着电路规模的增大，认证电路距离变得十分困难。在这项工作中，我们引入了距离放大器，这是一种模块化方法，用于增加量子低密度奇偶校验码的码距和认证的电路级保护。该构造将基础码与放大器进行张量积，并使其综合征提取电路适应于放大后的码。为了认证所得的存储器，我们开发了一种故障响应证书，该证书给出了电路距离的严格下界。合适的门排序和标志量子比特控制了相关错误，使我们能够建立明确的条件，在这些条件下，放大后的电路距离等于各组成电路距离的乘积。我们针对三种类型的放大器证明了这一乘法关系：带标志的$[[4,2,2]]$码、超图乘积码和旋转表面码。该证书可以递归扩展，因此在每一步放大中电路距离都精确相乘。例如，将带标志的$[[4,2,2]]$放大器连续应用四次到$[[18,4,4]]$种子码上，得到一个$[[13320,64,64]]$码，其电路距离$d_{\mathrm{circ}} \geq 48$，校验权重$w \leq 14$。我们进一步展示了如何通过放大显式跟踪单个逻辑量子比特。通过使高距离量子存储器能够从较小的构建块构建和认证，我们的框架为可扩展的容错量子计算提供了一条系统化的路径。
英文摘要
A large code distance does not by itself guarantee a well-protected quantum memory, as faults during syndrome extraction can propagate into correlated data errors. Certifying circuit distance becomes demanding as circuits grow. In this work, we introduce distance amplifiers, a modular approach to increasing both code distance and certified circuit-level protection in quantum low-density parity-check codes. The construction tensors a base code with an amplifier, adapting their syndrome-extraction circuits to the amplified code. To certify the resulting memory, we develop a fault-response certificate that yields rigorous lower bounds on circuit distance. Suitable gate ordering and flag qubits control correlated errors, allowing us to establish explicit conditions under which the amplified circuit distance equals the product of the constituent circuit distances. We prove this multiplicative relation for three types of amplifiers: the flagged $[[4,2,2]]$, hypergraph-product, and rotated surface codes. The certificate extends recursively, so the circuit distance multiplies exactly at every amplification step. For example, four successive applications of the flagged $[[4,2,2]]$ amplifier to a $[[18,4,4]]$ seed yield a $[[13320,64,64]]$ code with the circuit distance $d_{\mathrm{circ}} \geq 48$ and check weights $w \leq 14$. We further show how individual logical qubits can be tracked explicitly through amplification. By enabling high-distance quantum memories to be built and certified from smaller building blocks, our framework offers a systematic route toward scalable fault-tolerant quantum computing.
Commentsinitial commit, 26 pages and 5 figures
