静态表面码上无资源魔法轴测量的条件不可能性
A conditional no-go for resource-free magic-axis measurement on a static surface code
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中文总结 AI 辅助
研究静态表面码上无资源魔法轴测量的条件不可能性，通过检验普遍认知，证明单个稳定器测量记录及特定模型下协议的情况，分离开放假设并给出阈值，最终只剩一个猜想。
中文摘要 AI 辅助
在特定假设下，一个不添加折叠或自对偶结构的静态表面码补丁无法执行魔法态培育所依赖的魔法轴检查，尽管通常会被接受。这是一种条件不可能性。容错机器在制备魔法态上花费大量成本，培育通过测量魔法轴来实现，而每个已知构造都通过折叠或自对偶补丁来完成，人们通常认为这是必要的。我们检验了这种普遍认知。这种不可能性表明有用的检查必须在某处为魔法轴付出代价。它可以添加电荷转换资源，离开其接受历史的稀释状态，或者仅以指数级罕见的频率被接受。对于单个稳定器测量记录，从接受结果的拓扑解读直接证明了这一点。对于有界深度（多项式时空体积）模型中的自适应、后选择协议，在两个结构假设和一个亚临界假设下成立。我们分离出一个开放假设，表明仅靠保护不会强制它成立，并给出任何解决方案必须解决的阈值。剩下的只是一个猜想。
英文摘要
Under stated assumptions, a static surface-code patch that adds no fold or \mbox{self-dual} structure cannot perform the magic-axis check that magic-state cultivation relies on while still accepting often. This is a conditional no-go. Fault-tolerant machines spend much of their cost making magic states, and cultivation makes them in place by measuring the magic axis, which every known construction does through a fold or \mbox{self-dual} patch that it is folklore to call necessary. We test the folklore. The no-go says that a useful check must pay for the magic axis somewhere. It can add a charge-converting resource, it can leave the dilute regime of its accepted history, or it can accept only exponentially rarely. For a single stabilizer-measurement transcript this is proved outright, from a topological reading of the accepted outcome. For adaptive, post-selected protocols in a bounded-depth (polynomial spacetime-volume) model, it holds under two structural assumptions plus a subcriticality assumption. We isolate the one open assumption, show that protection alone does not force it, and give the threshold any resolution must address. What remains is a single conjecture.
