发表机构
Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究弱信号下量子码字识别问题，证明使用持久量子存储器可超越经典记忆接收器，实现纠错和抗噪，并给出具体码族和资源开销。
AI 中文摘要
考虑以下任务：通过一系列弱相位相互作用（每个相互作用编码一个比特）识别传递到量子传感器量子比特寄存器中的未知经典码字。假设每个接收比特控制一个相同的 $Z$-旋转角度 $\theta$，该旋转应用于每个传感器量子比特；接收器还可以在总量子比特预算 $Q$ 内使用辅助量子比特，在每次接收步骤中允许所有量子比特之间进行任意控制酉操作和纠缠。当收集到的总信号较弱（$Q\theta \rightarrow 0$）时，我们证明，与具有相同 $Q$ 和 $\theta$ 但仅在接收比特之间具有经典记忆的任何接收器相比，耦合到持久量子存储器的传感器可以更可靠地识别原始码字，即使在传输过程中发生比特翻转也是如此。特别地，对于具有偶数 $k$ 和 $n=2^k-1$ 的 $[n,k]$ 二元单纯形码族，我们通过将传感器寄存器耦合到相同大小的持久量子存储器，使用 $Q = \Theta((t+1)\log n)$ 和 $\theta=\frac{2\pi}{k\sqrt{n+1}}$，实现了对最多 $t\leq(k-2)/4$ 个传输错误的精确校正；对于 $t=o(\sqrt k)$，每个仅具有经典记忆的类似接收器的平均成功概率（在均匀选择的码字上）趋向于零。此外，在任意固定概率 $p<1/16$ 的独立比特翻转下，我们带有持久量子存储器的接收器使用 $Q=O(\log n\log\log n)$ 总量子比特和相同的 $\theta$，在 $n\to\infty$ 时实现解码错误趋向于零。相比之下，在相同的随机错误模型下，每个仅具有经典记忆的等效接收器的平均成功概率都趋向于零。
英文摘要
Consider the task of identifying an unknown classical codeword delivered to a register of quantum sensor qubits through a sequence of weak phase interactions that each encode one bit. Suppose that each received bit controls an identical $Z$-rotation of angle $θ$ applied to every sensor qubit; receivers may also use auxiliary qubits within a total qubit budget $Q$, with arbitrary control unitaries and entanglement among all qubits allowed during each reception step. When the total collected signal is weak ($Qθ\rightarrow 0$), we establish that a sensor coupled to a persistent quantum memory can identify the original codeword more reliably than any receiver with the same $Q$ and $θ$ but only classical memory between received bits, even when bit flips occur during transmission. In particular, for a family of $[n,k]$ binary simplex codes with even $k$ and $n=2^k-1$, we achieve exact correction of up to $t\leq(k-2)/4$ transmission errors by coupling the sensor register to a persistent quantum memory of the same size, using $Q = Θ((t+1)\log n)$ and $θ=\frac{2π}{k\sqrt{n+1}}$; for $t=o(\sqrt k)$, every comparable receiver with only classical memory instead has average success probability (over uniformly chosen codewords) tending to zero. Furthermore, under independent bit flips of any fixed probability $p<1/16$, our receiver with persistent quantum memory achieves decoding error tending to zero as $n\to\infty$ using $Q=O(\log n\log\log n)$ total qubits and the same $θ$. In contrast, every otherwise equivalent receiver with only classical memory has vanishing average success probability under the same stochastic error model.
Comments22 pages (13 figures)
