标题： 可访问的量子门在经典稳定子码上 显示英文标题

标题： Accessible Quantum Gates on Classical Stabilizer Codes

摘要： 随着具有强噪声偏置的物理量子位的出现，识别哪些量子门可以在针对单一主要错误类型的纠错码上高效实现变得越来越相关。 在这里，我们考虑针对比特翻转错误的$[n,k,d]$类经典稳定子码，其中$n$、$k$和$d$分别是物理量子位数、逻辑量子位数和码距。 我们证明了实现通用逻辑门集所需的操作必然需要复杂的酉电路来实现。 具体而言，这些实现电路要么由$h$层$r$-横穿操作组成，在$c$代码块上进行，使得$c^{h-1}r^h \geq d$，要么由$h$个门组成，每个门最多在同一个代码块上的$r$个物理量子比特上操作，使得$hr\geq d$。 类似的约束不仅适用于设计用于纠正相位翻转错误的经典码，也适用于针对偏置噪声定制的量子稳定子码。 这促使我们更仔细地检查使用例如~魔术态纯化和在偏置噪声稳定子码框架内的培育来构建替代逻辑门的方法。 显示英文摘要

摘要： With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type. Here, we consider $[n,k,d]$-classical stabilizer codes addressing bit-flip errors where $n$, $k$ and $d$ are the numbers of physical and logical qubits, and the code distance respectively. We prove that operations essential for achieving a universal logical gate set necessarily require complex unitary circuits to be implemented. Specifically, these implementation circuits either consists of $h$ layers of $r$-transversal operations on $c$ codeblocks such that $c^{h-1}r^h \geq d$ or of $h$ gates, each operating on at most $r$ physical qubits on the same codeblock, such that $hr\geq d$. Similar constraints apply not only to classical codes designed to correct phase-flip errors, but also to quantum stabilizer codes tailored to biased noise. This motivates a closer examination of alternative logical gate constructions using eg.~magic state distillation and cultivation within the framework of biased-noise stabilizer codes.