发表机构
Universität Siegen; Sandia National Laboratories; University of New Mexico; Leiden University（锡根大学; 桑迪亚国家实验室; 新墨西哥大学; 莱顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对量子计算中的融合策略问题，刻画了k=1量子比特编码下的完美融合策略，证明其普适性并解答开放问题，还为新图参数提供操作解释。
AI 中文摘要
逻辑融合在量子信息的诸多任务中十分重要，例如量子纠错和量子中继器。在光子学场景中，必须应对物理融合具有概率性的事实（即相关量子比特在乘积基下被测量），这一过程会根据失败情况和相关基的不同，可能导致逻辑层面的失败。每个量子比特的失败基选择被称为融合策略，寻找优良的融合策略对于优化基于融合的量子计算的性能至关重要。在此，我们对编码k=1个量子比特的情况给出完整刻画，特别是刻画那些代码和融合策略，使得除一个物理融合外其余均可失败，即“完美融合策略”。在此过程中，我们重现了先前已知的完美融合策略，并找到了量子奇偶校验码的完美融合策略，回答了一个开放问题。我们还证明完美融合策略具有普适性：随机[[n,1,d]]图码以指数级接近1的概率拥有完美融合策略。此外，我们通过对图的一个新参数（即所有LC等价图中某顶点的最大度）给出新的操作上有意义的解释，为该参数的研究提供了动机。
英文摘要
Logical fusions are important for a number of tasks in quantum information, such as quantum error correction and quantum repeaters. In the photonic setting one must contend with the fact that physical fusions can fail, i.e. individual qubits are measured in a user-controlled product state basis with some probability, which can lead to a failure on the logical level. The choice of failure basis of each qubit is known as a fusion strategy, and finding good fusion strategies is important for optimizing performance of fusion-based quantum computation. Here we provide a complete characterization when $k=1$ qubits are encoded, and in particular characterize those codes and fusion strategies such that all but one physical fusion can fail, i.e.~\emph{perfect fusion strategies}. In doing so, we recover previously known perfect fusion strategies, and find perfect fusion strategies for quantum parity-check codes, answering an open question. We furthermore show that perfect fusion strategies are generic: random $[[n, 1, d]]$ graph codes admit a perfect fusion strategy with probability exponentially close to $1$. Additionally we motivate the study of a new graph parameter, namely the maximum degree of a graph at a given vertex taken over all LC-equivalent graphs, by giving a new operationally meaningful interpretation of it.
